subject:(Contact manifolds)

Michigan State University

1. Kasebian, Kaveh. Concave fillings and branched covers.

Degree: 2018, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:16402

►

Thesis Ph. D. Michigan State University. Mathematics 2018

This dissertation contains two results. The first result involves concave symplectic struc-tures on a neighborhood of certain… (more)

Subjects/Keywords: Contact manifolds; Mathematics

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APA (6^th Edition):

Kasebian, K. (2018). Concave fillings and branched covers. (Thesis). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:16402

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Kasebian, Kaveh. “Concave fillings and branched covers.” 2018. Thesis, Michigan State University. Accessed March 08, 2021. http://etd.lib.msu.edu/islandora/object/etd:16402.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Kasebian, Kaveh. “Concave fillings and branched covers.” 2018. Web. 08 Mar 2021.

Vancouver:

Kasebian K. Concave fillings and branched covers. [Internet] [Thesis]. Michigan State University; 2018. [cited 2021 Mar 08]. Available from: http://etd.lib.msu.edu/islandora/object/etd:16402.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Kasebian K. Concave fillings and branched covers. [Thesis]. Michigan State University; 2018. Available from: http://etd.lib.msu.edu/islandora/object/etd:16402

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Aberdeen

2. Spáčil, Oldřich. On the Chern-Weil theory for transformation groups of contact manifolds.

Degree: PhD, 2014, University of Aberdeen

URL: https://abdn.alma.exlibrisgroup.com/view/delivery/44ABE_INST/12153235850005941 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619183

► The thesis deals with contact manifolds and their groups of transformations and relatedly with contact fibre bundles. We apply the framework of convenient calculus on… (more)

Subjects/Keywords: 510; Transformation groups; Contact manifolds

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APA (6^th Edition):

Spáčil, O. (2014). On the Chern-Weil theory for transformation groups of contact manifolds. (Doctoral Dissertation). University of Aberdeen. Retrieved from https://abdn.alma.exlibrisgroup.com/view/delivery/44ABE_INST/12153235850005941 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619183

Chicago Manual of Style (16^th Edition):

Spáčil, Oldřich. “On the Chern-Weil theory for transformation groups of contact manifolds.” 2014. Doctoral Dissertation, University of Aberdeen. Accessed March 08, 2021. https://abdn.alma.exlibrisgroup.com/view/delivery/44ABE_INST/12153235850005941 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619183.

MLA Handbook (7^th Edition):

Spáčil, Oldřich. “On the Chern-Weil theory for transformation groups of contact manifolds.” 2014. Web. 08 Mar 2021.

Vancouver:

Spáčil O. On the Chern-Weil theory for transformation groups of contact manifolds. [Internet] [Doctoral dissertation]. University of Aberdeen; 2014. [cited 2021 Mar 08]. Available from: https://abdn.alma.exlibrisgroup.com/view/delivery/44ABE_INST/12153235850005941 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619183.

Council of Science Editors:

Spáčil O. On the Chern-Weil theory for transformation groups of contact manifolds. [Doctoral Dissertation]. University of Aberdeen; 2014. Available from: https://abdn.alma.exlibrisgroup.com/view/delivery/44ABE_INST/12153235850005941 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619183

Georgia Tech

3. Tosun, Bulent. Legendrian and transverse knots and their invariants.

Degree: PhD, Mathematics, 2012, Georgia Tech

URL: http://hdl.handle.net/1853/44880

► In this thesis, we study Legendrian and transverse isotopy problem for cabled knot types. We give two structural theorems to describe when the (r,s)- cable… (more)

Subjects/Keywords: Knots in contact geometry. cabling; Knot theory; Contact manifolds

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APA (6^th Edition):

Tosun, B. (2012). Legendrian and transverse knots and their invariants. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/44880

Chicago Manual of Style (16^th Edition):

Tosun, Bulent. “Legendrian and transverse knots and their invariants.” 2012. Doctoral Dissertation, Georgia Tech. Accessed March 08, 2021. http://hdl.handle.net/1853/44880.

MLA Handbook (7^th Edition):

Tosun, Bulent. “Legendrian and transverse knots and their invariants.” 2012. Web. 08 Mar 2021.

Vancouver:

Tosun B. Legendrian and transverse knots and their invariants. [Internet] [Doctoral dissertation]. Georgia Tech; 2012. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/1853/44880.

Council of Science Editors:

Tosun B. Legendrian and transverse knots and their invariants. [Doctoral Dissertation]. Georgia Tech; 2012. Available from: http://hdl.handle.net/1853/44880

University of Southern California

4. Golovko, Roman. The embedded contact homology of S1xD2.

Degree: PhD, Mathematics, 2009, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/236216/rec/6686

► The goal of this thesis is to understand generalizations of (cylindrical) contact homology and embedded contact homology to contact 3-manifolds with sutured boundary. Both contact… (more)

Subjects/Keywords: embedded contact homology; sutured contact manifolds

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APA (6^th Edition):

Golovko, R. (2009). The embedded contact homology of S1xD2. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/236216/rec/6686

Chicago Manual of Style (16^th Edition):

Golovko, Roman. “The embedded contact homology of S1xD2.” 2009. Doctoral Dissertation, University of Southern California. Accessed March 08, 2021. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/236216/rec/6686.

MLA Handbook (7^th Edition):

Golovko, Roman. “The embedded contact homology of S1xD2.” 2009. Web. 08 Mar 2021.

Vancouver:

Golovko R. The embedded contact homology of S1xD2. [Internet] [Doctoral dissertation]. University of Southern California; 2009. [cited 2021 Mar 08]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/236216/rec/6686.

Council of Science Editors:

Golovko R. The embedded contact homology of S1xD2. [Doctoral Dissertation]. University of Southern California; 2009. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/236216/rec/6686

5. Ahmad, Sharfuddin. On almost contact manifolds;.

Degree: Mathematics, 1977, Aligarh Muslim University

URL: http://shodhganga.inflibnet.ac.in/handle/10603/53120

Abstract not available newline newline

Bibliography p. 89-92

Advisors/Committee Members: Ishar Husain, S.

Subjects/Keywords: Contact Manifolds; Curvature Tensor; Connexions

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APA (6^th Edition):

Ahmad, S. (1977). On almost contact manifolds;. (Thesis). Aligarh Muslim University. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/53120

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ahmad, Sharfuddin. “On almost contact manifolds;.” 1977. Thesis, Aligarh Muslim University. Accessed March 08, 2021. http://shodhganga.inflibnet.ac.in/handle/10603/53120.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ahmad, Sharfuddin. “On almost contact manifolds;.” 1977. Web. 08 Mar 2021.

Vancouver:

Ahmad S. On almost contact manifolds;. [Internet] [Thesis]. Aligarh Muslim University; 1977. [cited 2021 Mar 08]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/53120.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ahmad S. On almost contact manifolds;. [Thesis]. Aligarh Muslim University; 1977. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/53120

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

6. Ahmad, Sharfuddin. On almost contact manifolds;.

Degree: Mathematics, 1977, Aligarh Muslim University

URL: http://shodhganga.inflibnet.ac.in/handle/10603/52218

Abstract not available newline newline

Bibliography p. 89-92

Advisors/Committee Members: Ishar Husain, S.

Subjects/Keywords: Contact Manifolds; Curvature Tensor; Connexions

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ahmad, S. (1977). On almost contact manifolds;. (Thesis). Aligarh Muslim University. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/52218

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ahmad, Sharfuddin. “On almost contact manifolds;.” 1977. Thesis, Aligarh Muslim University. Accessed March 08, 2021. http://shodhganga.inflibnet.ac.in/handle/10603/52218.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ahmad, Sharfuddin. “On almost contact manifolds;.” 1977. Web. 08 Mar 2021.

Vancouver:

Ahmad S. On almost contact manifolds;. [Internet] [Thesis]. Aligarh Muslim University; 1977. [cited 2021 Mar 08]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/52218.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ahmad S. On almost contact manifolds;. [Thesis]. Aligarh Muslim University; 1977. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/52218

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

7. Μάρκελλος, Μιχαήλ. Μελέτη ειδικών κατηγοριών πολλαπλοτήτων επαφής Riemann.

Degree: 2009, University of Patras

URL: http://nemertes.lis.upatras.gr/jspui/handle/10889/2705

►

Το κύριο αντικείμενο της διατριβής συνίσταται στη μελέτη της γεωμετρίας των τρισδιάστατων H-μετρικών πολλαπλοτήτων επαφής, ή, ισοδύναμα, των μετρικών πολλαπλοτήτων επαφής για τις οποίες το… (more)

▼

Το κύριο αντικείμενο της διατριβής συνίσταται στη μελέτη της γεωμετρίας των τρισδιάστατων H-μετρικών πολλαπλοτήτων επαφής, ή, ισοδύναμα, των μετρικών πολλαπλοτήτων επαφής για τις οποίες το διανυσματικό πεδίο ξ είναι πεδίο ιδιοδιανυσμάτων του τελεστή Ricci Q. Συγκεκριμένα, αποδεικνύεται ότι μια τρισδιάστατη H-μετρική πολλαπλότητα επαφής [Μ, (η, ξ, φ, g)] χαρακτηρίζεται γεωμετρικά από μια συνθήκη που εμπλέκει τον τανυστή καμπυλότητας της Μ και τρεις διαφορίσιμες συναρτήσεις κ, μ και ν της Μ. Η συνθήκη αυτή οδηγεί στην εισαγωγή μιας νέας κλάσης μετρικών πολλαπλοτήτων επαφής: τις (κ, μ, ν)-πολλαπλότητες επαφής. Το ενδιαφέρον με τις (κ, μ, ν)-πολλαπλότητες επαφής είναι ότι για διάσταση μεγαλύτερη του τρία εκφυλίζονται στις (κ, μ)-πολλαπλότητες επαφής, δηλαδή, οι συναρτήσεις κ, μ είναι σταθερές και η συνάρτηση ν είναι η μηδενική συνάρτηση. Αντιθέτως, αποδεικνύεται ότι τέτοιες μετρικές πολλαπλότητες επαφής υπάρχουν στη διάσταση τρία. Ένα άλλο από τα προβλήματα που εξετάζονται σ' αυτή τη διατριβή είναι ο χαρακτηρισμός των διαρμονικών καμπυλών του Legendre και των αντι-αναλλοίωτων επιφανειών εμβυθισμένων σε τρισδιάστατες (κ, μ, ν)-πολλαπλότητες επαφής. Συγκεκριμένα, αποδεικνύεται ότι οι διαρμονικές καμπύλες του Legendre είναι οι γεωδαισιακές αυτών των χώρων. Επιπλέον, αποδεικνύεται ότι οι διαρμονικές και χωρίς ελαχιστικά σημεία αντι-αναλλοίωτες επιφάνειες που είναι εμβυθισμένες σε τρισδιάστατες γενικευμένες (κ, μ)-πολλαπλότητες επαφής και των οποίων το μέτρο του διανυσματικού πεδίου της μέσης καμπυλότητας είναι σταθερό, είναι τοπικά Ευκλείδειες.

The main object of this Doctoral Thesis is the study of the geometry of 3-dimensional H-contact metric manifolds, or, equivalently, the contact metric manifolds whose the vector field ξ is an eigenvector of the Ricci operator Q. More precisely, it is proved that 3-dimensional H-contact metric manifolds [M, (η, ξ, φ, g)] are geometrically characterized by a specific curvature condition and three differentiable functions κ, μ and ν of M. This condition leads to the introduction of a new class of contact metric manifolds: the (κ, μ, ν)-contact metric manifolds. It is remarkable that for dimension greater than three, such manifolds are reduced to (κ, μ)-contact metric manifolds, i.e. the functions κ, μ are constants and the function ν is the zero function. On the contrary, in three dimension (κ,μ,ν)-contact metric manifolds exist. Another problem which is studied is the classification of biharmonic Legendre curves and anti-invariant surfaces immersed in 3-dimensional (κ, μ, ν)-contact metric manifolds. It is proved that biharmonic Legendre curves in 3-dimensional (κ, μ, ν)-contact metric manifolds are necessarily geodesics. Furthermore, it is proved that biharmonic and without minimal points anti-invariant surfaces immersed in 3-dimensional generalized (κ, μ)-contact metric manifolds with constant norm of the mean curvature vector field, are locally flat.

Advisors/Committee Members: Παπαντωνίου, Βασίλειος, Παπαντωνίου, Βασίλειος, Κουφογιώργος, Θεμιστοκλής, Ξένος, Φίλιππος, Κοτσιώλης, Αθανάσιος, Μπαικούσης, Χρήστος, Γουλή - Ανδρέου, Φλωρεντία, Αρβανιτογεώργος, Ανδρέας.

Subjects/Keywords: Μετρικές πολλαπλότητες επαφής; Η-μετρικές πολλαπλότητες επαφής; (κ, μ, ν)-μετρικές πολλαπλότητες επαφής; Γενικευμένες (κ, μ)-πολλαπλότητες επαφής; Αρμονικές απεικονίσεις; Διαρμονικές απεικονίσεις; 516.373; Contact metric manifolds; H-contact metric manifolds; (κ, μ, ν)-contact metric manifolds; Generalized (κ, μ)-contact metric manifolds; Harmonic maps; Biharmonic maps

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Μάρκελλος, �. (2009). Μελέτη ειδικών κατηγοριών πολλαπλοτήτων επαφής Riemann. (Doctoral Dissertation). University of Patras. Retrieved from http://nemertes.lis.upatras.gr/jspui/handle/10889/2705

Chicago Manual of Style (16^th Edition):

Μάρκελλος, Μιχαήλ. “Μελέτη ειδικών κατηγοριών πολλαπλοτήτων επαφής Riemann.” 2009. Doctoral Dissertation, University of Patras. Accessed March 08, 2021. http://nemertes.lis.upatras.gr/jspui/handle/10889/2705.

MLA Handbook (7^th Edition):

Μάρκελλος, Μιχαήλ. “Μελέτη ειδικών κατηγοριών πολλαπλοτήτων επαφής Riemann.” 2009. Web. 08 Mar 2021.

Vancouver:

Μάρκελλος �. Μελέτη ειδικών κατηγοριών πολλαπλοτήτων επαφής Riemann. [Internet] [Doctoral dissertation]. University of Patras; 2009. [cited 2021 Mar 08]. Available from: http://nemertes.lis.upatras.gr/jspui/handle/10889/2705.

Council of Science Editors:

Μάρκελλος �. Μελέτη ειδικών κατηγοριών πολλαπλοτήτων επαφής Riemann. [Doctoral Dissertation]. University of Patras; 2009. Available from: http://nemertes.lis.upatras.gr/jspui/handle/10889/2705

University of Aberdeen

8. Spáčil, Oldřich.; University of Aberdeen.Dept. of Mathematics. On the Chern-Weil theory for transformation groups of contact manifolds.

Degree: Dept. of Mathematics., 2014, University of Aberdeen

URL: http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?application=DIGITOOL-3&owner=resourcediscovery&custom_att_2=simple_viewer&pid=211433 ; http://digitool.abdn.ac.uk:1801/webclient/DeliveryManager?pid=211433&custom_att_2=simple_viewer

Subjects/Keywords: Transformation groups.; Contact manifolds.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Spáčil, O. ;. U. o. A. D. o. M. (2014). On the Chern-Weil theory for transformation groups of contact manifolds. (Doctoral Dissertation). University of Aberdeen. Retrieved from http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?application=DIGITOOL-3&owner=resourcediscovery&custom_att_2=simple_viewer&pid=211433 ; http://digitool.abdn.ac.uk:1801/webclient/DeliveryManager?pid=211433&custom_att_2=simple_viewer

Chicago Manual of Style (16^th Edition):

Spáčil, Oldřich ; University of Aberdeen Dept of Mathematics. “On the Chern-Weil theory for transformation groups of contact manifolds.” 2014. Doctoral Dissertation, University of Aberdeen. Accessed March 08, 2021. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?application=DIGITOOL-3&owner=resourcediscovery&custom_att_2=simple_viewer&pid=211433 ; http://digitool.abdn.ac.uk:1801/webclient/DeliveryManager?pid=211433&custom_att_2=simple_viewer.

MLA Handbook (7^th Edition):

Spáčil, Oldřich ; University of Aberdeen Dept of Mathematics. “On the Chern-Weil theory for transformation groups of contact manifolds.” 2014. Web. 08 Mar 2021.

Vancouver:

Spáčil O;UoADoM. On the Chern-Weil theory for transformation groups of contact manifolds. [Internet] [Doctoral dissertation]. University of Aberdeen; 2014. [cited 2021 Mar 08]. Available from: http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?application=DIGITOOL-3&owner=resourcediscovery&custom_att_2=simple_viewer&pid=211433 ; http://digitool.abdn.ac.uk:1801/webclient/DeliveryManager?pid=211433&custom_att_2=simple_viewer.

Council of Science Editors:

Spáčil O;UoADoM. On the Chern-Weil theory for transformation groups of contact manifolds. [Doctoral Dissertation]. University of Aberdeen; 2014. Available from: http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?application=DIGITOOL-3&owner=resourcediscovery&custom_att_2=simple_viewer&pid=211433 ; http://digitool.abdn.ac.uk:1801/webclient/DeliveryManager?pid=211433&custom_att_2=simple_viewer

Georgia Tech

9. Conway, James. Transverse surgery on knots in contact three-manifolds.

Degree: PhD, Mathematics, 2016, Georgia Tech

URL: http://hdl.handle.net/1853/55563

► We study the effect of surgery on transverse knots in contact 3-manifolds by examining its effect on open books, the Heegaard Floer contact invariant, and… (more)

Subjects/Keywords: Contact geometry; Geometric topology; Knot theory; 3-manifolds; Topology; Geometry

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APA (6^th Edition):

Conway, J. (2016). Transverse surgery on knots in contact three-manifolds. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/55563

Chicago Manual of Style (16^th Edition):

Conway, James. “Transverse surgery on knots in contact three-manifolds.” 2016. Doctoral Dissertation, Georgia Tech. Accessed March 08, 2021. http://hdl.handle.net/1853/55563.

MLA Handbook (7^th Edition):

Conway, James. “Transverse surgery on knots in contact three-manifolds.” 2016. Web. 08 Mar 2021.

Vancouver:

Conway J. Transverse surgery on knots in contact three-manifolds. [Internet] [Doctoral dissertation]. Georgia Tech; 2016. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/1853/55563.

Council of Science Editors:

Conway J. Transverse surgery on knots in contact three-manifolds. [Doctoral Dissertation]. Georgia Tech; 2016. Available from: http://hdl.handle.net/1853/55563

Michigan State University

10. Arıkan, Mehmet Fırat. Topological invariants of contact structures and planar open books.

Degree: PhD, Department of Mathematics, 2008, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:39191

Subjects/Keywords: Decomposition (Mathematics); Three-manifolds (Topology); Contact manifolds

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Arıkan, M. F. (2008). Topological invariants of contact structures and planar open books. (Doctoral Dissertation). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:39191

Chicago Manual of Style (16^th Edition):

Arıkan, Mehmet Fırat. “Topological invariants of contact structures and planar open books.” 2008. Doctoral Dissertation, Michigan State University. Accessed March 08, 2021. http://etd.lib.msu.edu/islandora/object/etd:39191.

MLA Handbook (7^th Edition):

Arıkan, Mehmet Fırat. “Topological invariants of contact structures and planar open books.” 2008. Web. 08 Mar 2021.

Vancouver:

Arıkan MF. Topological invariants of contact structures and planar open books. [Internet] [Doctoral dissertation]. Michigan State University; 2008. [cited 2021 Mar 08]. Available from: http://etd.lib.msu.edu/islandora/object/etd:39191.

Council of Science Editors:

Arıkan MF. Topological invariants of contact structures and planar open books. [Doctoral Dissertation]. Michigan State University; 2008. Available from: http://etd.lib.msu.edu/islandora/object/etd:39191

11. Courte, Sylvain. H-cobordismes en géométrie symplectique : H-cobordisms in symplectic geometry.

Degree: Docteur es, Mathématiques, 2015, Lyon, École normale supérieure

URL: http://www.theses.fr/2015ENSL0991

►

À toute variété de contact, on peut associer canoniquement une variété symplectique appelée sa symplectisation de sorte que la géométrie de contact peut se reformuler… (more)

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À toute variété de contact, on peut associer canoniquement une variété symplectique appelée sa symplectisation de sorte que la géométrie de contact peut se reformuler en termes de géométrie symplectique équivariante. Au sujet de cette construction fondamentale, une question basique restait ouverte : si deux variété de contact ont des symplectisations isomorphes sont-elles isomorphes ? On construit dans cette thèse des contre-exemples à cette question. Il existe en effet, en toute dimension impaire supérieure ou égale à 5, des variétés de contact non difféomorphes admettant pourtant des symplectisations isomorphes. On construit également, sur une même variété deux structures de contact non conjuguées par un difféomorphisme mais admettant des symplectisations isomorphes. Les démonstrations sont basées sur un phénomène bien connu en topologie différentielle (l'existence de h-cobordismes non triviaux, détectée par la torsion de Whitehead) ainsi que sur des résultats de flexibilité en géométrie symplectique dus à Cieliebak et Eliashberg. Un autre résultat de cette th?e affirme que ces variété de contact, bien que non isomorphes, le deviennent toutefois après un nombre suffisant de sommes connexes avec un produit de sphères.

To any contact manifold one can associate a symplectic manifold called its symplectisation in such a way that contact geometry can be reformulated in terms of equivariant symplectic geometry. Concerning this fundamental construction, a basic question remained open : if two contact manifolds have isomorphic symplectizations, are they isomorphic ? In this thesis, we construct counter-examples to this question. Indeed, in any odd dimension greater than or equal to 5, there exist non-diffeomorphic contact manifolds with isomorphic symplectisations. In addition, we construct two contact structures on a closed manifold that are not conjugate by a diffeomorphism though their symplectizations are isomorphic. The proofs are based on a well-known phenomenon in differential topology (the existence of non-trivial h-cobordisms, detected by Whitehead torsion) as well as flexibility results in symplectic geometry due to Cieliebak and Eliashberg. Another result from this thesis asserts that though these contact manifolds are not isomorphic, they become so after sufficiently many connect sum with a product of spheres.

Advisors/Committee Members: Giroux, Emmanuel (thesis director).

Subjects/Keywords: Variétés de contact; Variétés symplectiques; Symplectisation; Cobordismes de Weinstein; H-principe; H-cobordismes; Torsion de Whitehead; Contact manifolds; Symplectic manifolds; Symplectization; Weinstein cobordisms; H-principle; H-cobordisms; Whitehead torsion

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Courte, S. (2015). H-cobordismes en géométrie symplectique : H-cobordisms in symplectic geometry. (Doctoral Dissertation). Lyon, École normale supérieure. Retrieved from http://www.theses.fr/2015ENSL0991

Chicago Manual of Style (16^th Edition):

Courte, Sylvain. “H-cobordismes en géométrie symplectique : H-cobordisms in symplectic geometry.” 2015. Doctoral Dissertation, Lyon, École normale supérieure. Accessed March 08, 2021. http://www.theses.fr/2015ENSL0991.

MLA Handbook (7^th Edition):

Courte, Sylvain. “H-cobordismes en géométrie symplectique : H-cobordisms in symplectic geometry.” 2015. Web. 08 Mar 2021.

Vancouver:

Courte S. H-cobordismes en géométrie symplectique : H-cobordisms in symplectic geometry. [Internet] [Doctoral dissertation]. Lyon, École normale supérieure; 2015. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2015ENSL0991.

Council of Science Editors:

Courte S. H-cobordismes en géométrie symplectique : H-cobordisms in symplectic geometry. [Doctoral Dissertation]. Lyon, École normale supérieure; 2015. Available from: http://www.theses.fr/2015ENSL0991

Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)

12. Τσολακίδου, Νίκη. Μελέτη μετρικών πολλαπλοτήτων επαφής με τη βοήθεια τανυστών καμπυλότητας.

Degree: 2002, Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)

URL: http://hdl.handle.net/10442/hedi/15078

►

A contact manifold is a C? ? manifold M2n+1 equipped with a global 1? form η , called the contact form, such that ? (… (more)

▼

A contact manifold is a C? ? manifold M2n+1 equipped with a global 1? form η , called the contact form, such that ? ( ) ? 0 n η dη everywhere on M2n+1. The study of contact manifolds, from a global point of view, has been developed in the last 50 years, starting from the work of G.Reeb on properties of the trajectories of dynamical systems. The contact structures find applications in analytic mechanics and in the quantization theory of B.Kostant and J.-M.Souriau. S.Sasaki introduced a natural metric assosiated to a contact structure. The set of assosiated metrics to η is of infinite dimension. In this thesis we classify two subclasses of contact metric manifolds. In the first chapter the definitions and the basic properties of conceptions which appear in the study are refered. In the second chapter we study conformally flat contact metric manifolds M2n+1(? ,ξ ,η , g) (n > 1) with# = ?k? 2 , (## := R(?,ξ )ξ ), where k is a smooth function on M2n+1. We prove that these manifolds are Sasakian of constant curvature 1. In the third chapter we study conformally flat contact metric manifolds M2n+1(? ,ξ ,η , g) (n > 1) withQξ = ρξ , where ρ is a smooth function on M2n+1. We prove that these manifolds are Sasakian of constant curvature 1.

Μία πολλαπλότητα επαφής είναι μία C? ? πολλαπλότητα M2n+1, η οποία φέρει μία ολικά ορισμένη 1? μορφή η τέτοια, ώστε ? ( )n ? 0 η dη παντού στη M2n+1. Η μελέτη των πολλαπλοτήτων επαφής από ολική άποψη αναπτύχθηκε τα τελευταία 50 χρόνια ξεκινώντας από την εργασία του G.Reeb επί των ιδιοτήτων των τροχιών των δυναμικών συστημάτων. Οι δομές επαφής έχουν εφαρμογές στην αναλυτική μηχανική και τη θεωρία κβαντοποίησης των B.Kostant και J.-M.Souriau. Πρώτος ο S.Sasaki εισήγαγε με φυσικό τρόπο μία μετρική προσαρτημένη στη δομή επαφής. Ο χώρος των μετρικών των προσαρτημένων στη μορφή επαφής η είναι άπειρης διάστασης. Στην παρούσα διατριβή ασχολούμαστε με την ταξινόμηση δύο υποκλάσεων των μετρικών πολλαπλοτήτων επαφής. Στο πρώτο κεφάλαιο αναφέρονται οι ορισμοί και οι βασικές ιδιότητες των μαθηματικών εννοιών που εμφανίζονται στη μελέτη. Στο δεύτερο κεφάλαιο μελετώνται σύμμορφα επίπεδες μετρικές πολλαπλότητες επαφής M2n+1(? ,ξ ,η , g) (n > 1) με τη συνθήκη ## = ?k? 2 , (## := R(?,ξ )ξ), όπου η k είναι μία λεία συνάρτηση επί της M2n+1 και αποδεικνύεται ότι είναι πολλαπλότητες Sasaki σταθερής καμπυλότητας 1. Στο τρίτο κεφάλαιο μελετώνται σύμμορφα επίπεδες μετρικές πολλαπλότητες επαφής M2n+1(? ,ξ ,η , g) (n > 1) με τη συνθήκη Qξ = ρξ , όπου η ρ είναι μία λεία συνάρτηση επί της M2n+1 και αποδεικνύεται ότι είναι πολλαπλότητες Sasaki σταθερής καμπυλότητας 1.

Subjects/Keywords: Μετρικές πολλαπλότητες επαφής; Πολλαπλότητες του Riemann; Πολλαπλότητες κ-επαφής; Πολλαπλότητες Sasaki; Contact metric manifolds; Riemannian manifolds; K-contact manifolds; Sasakian manifolds

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Τσολακίδου, . �. (2002). Μελέτη μετρικών πολλαπλοτήτων επαφής με τη βοήθεια τανυστών καμπυλότητας. (Thesis). Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ). Retrieved from http://hdl.handle.net/10442/hedi/15078

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Τσολακίδου, Νίκη. “Μελέτη μετρικών πολλαπλοτήτων επαφής με τη βοήθεια τανυστών καμπυλότητας.” 2002. Thesis, Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ). Accessed March 08, 2021. http://hdl.handle.net/10442/hedi/15078.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Τσολακίδου, Νίκη. “Μελέτη μετρικών πολλαπλοτήτων επαφής με τη βοήθεια τανυστών καμπυλότητας.” 2002. Web. 08 Mar 2021.

Vancouver:

Τσολακίδου �. Μελέτη μετρικών πολλαπλοτήτων επαφής με τη βοήθεια τανυστών καμπυλότητας. [Internet] [Thesis]. Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); 2002. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10442/hedi/15078.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Τσολακίδου �. Μελέτη μετρικών πολλαπλοτήτων επαφής με τη βοήθεια τανυστών καμπυλότητας. [Thesis]. Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); 2002. Available from: http://hdl.handle.net/10442/hedi/15078

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Penn State University

13. Van Erp, Johannes. The Atiyah-Singer Index Formula for Subelliptic Operators on Contact Manifolds.

Degree: 2008, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/6880

► The Atiyah-Singer index theorem gives a topological formula for the index of an elliptic differential operator. The topological index depends on a cohomology class that… (more)

Subjects/Keywords: Index theory; Hypoelliptic operators; Contact manifolds

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APA (6^th Edition):

Van Erp, J. (2008). The Atiyah-Singer Index Formula for Subelliptic Operators on Contact Manifolds. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/6880

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Van Erp, Johannes. “The Atiyah-Singer Index Formula for Subelliptic Operators on Contact Manifolds.” 2008. Thesis, Penn State University. Accessed March 08, 2021. https://submit-etda.libraries.psu.edu/catalog/6880.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Van Erp, Johannes. “The Atiyah-Singer Index Formula for Subelliptic Operators on Contact Manifolds.” 2008. Web. 08 Mar 2021.

Vancouver:

Van Erp J. The Atiyah-Singer Index Formula for Subelliptic Operators on Contact Manifolds. [Internet] [Thesis]. Penn State University; 2008. [cited 2021 Mar 08]. Available from: https://submit-etda.libraries.psu.edu/catalog/6880.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Van Erp J. The Atiyah-Singer Index Formula for Subelliptic Operators on Contact Manifolds. [Thesis]. Penn State University; 2008. Available from: https://submit-etda.libraries.psu.edu/catalog/6880

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Massey University

14. Jayne, Nicola. Legendre foliations on contact metric manifolds.

Degree: PhD, Mathematics, 1992, Massey University

URL: http://hdl.handle.net/10179/3554

► This thesis develops the theory of Legendre foliations on contact manifolds by associating a contact metric structure with a contact manifold and investigating Legendre foliations… (more)

Subjects/Keywords: Legendre foliations; Contact manifolds; Legendre polynomials

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APA (6^th Edition):

Jayne, N. (1992). Legendre foliations on contact metric manifolds. (Doctoral Dissertation). Massey University. Retrieved from http://hdl.handle.net/10179/3554

Chicago Manual of Style (16^th Edition):

Jayne, Nicola. “Legendre foliations on contact metric manifolds.” 1992. Doctoral Dissertation, Massey University. Accessed March 08, 2021. http://hdl.handle.net/10179/3554.

MLA Handbook (7^th Edition):

Jayne, Nicola. “Legendre foliations on contact metric manifolds.” 1992. Web. 08 Mar 2021.

Vancouver:

Jayne N. Legendre foliations on contact metric manifolds. [Internet] [Doctoral dissertation]. Massey University; 1992. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10179/3554.

Council of Science Editors:

Jayne N. Legendre foliations on contact metric manifolds. [Doctoral Dissertation]. Massey University; 1992. Available from: http://hdl.handle.net/10179/3554

15. Μάρκελλος, Μιχαήλ. Ειδικές κατηγορίες πολλαπλοτήτων επαφής Riemann.

Degree: 2006, University of Patras

URL: http://nemertes.lis.upatras.gr/jspui/handle/10889/881

►

Στη μεταπτυχιακή αυτή διπλωματική εργασία, αρχικά εισάγουμε τις έννοιες των μετρικών πολλαπλοτήτων σχεδόν επαφής και των μετρικών πολλαπλοτήτων επαφής, δίνοντας και μερικά παραδείγματα από κάθε… (more)

Subjects/Keywords: Μετρικές πολλαπλότητες επαφής; Πολλαπλότητες Κ – επαφής; Πολλαπλότητες του Sasaki; (κ, μ) - πολλαπλότητες επαφής; Μετρικές πολλαπλότητες Η – επαφής; 512.73; Contact metric manifolds; K – contact manifolds; Sasakian manifolds; (κ, μ) – contact manifolds; H – contact metric manifolds

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Μάρκελλος, �. (2006). Ειδικές κατηγορίες πολλαπλοτήτων επαφής Riemann. (Masters Thesis). University of Patras. Retrieved from http://nemertes.lis.upatras.gr/jspui/handle/10889/881

Chicago Manual of Style (16^th Edition):

Μάρκελλος, Μιχαήλ. “Ειδικές κατηγορίες πολλαπλοτήτων επαφής Riemann.” 2006. Masters Thesis, University of Patras. Accessed March 08, 2021. http://nemertes.lis.upatras.gr/jspui/handle/10889/881.

MLA Handbook (7^th Edition):

Μάρκελλος, Μιχαήλ. “Ειδικές κατηγορίες πολλαπλοτήτων επαφής Riemann.” 2006. Web. 08 Mar 2021.

Vancouver:

Μάρκελλος �. Ειδικές κατηγορίες πολλαπλοτήτων επαφής Riemann. [Internet] [Masters thesis]. University of Patras; 2006. [cited 2021 Mar 08]. Available from: http://nemertes.lis.upatras.gr/jspui/handle/10889/881.

Council of Science Editors:

Μάρκελλος �. Ειδικές κατηγορίες πολλαπλοτήτων επαφής Riemann. [Masters Thesis]. University of Patras; 2006. Available from: http://nemertes.lis.upatras.gr/jspui/handle/10889/881

16. Casey, Meredith Perrie. Branched covers of contact manifolds.

Degree: PhD, Mathematics, 2013, Georgia Tech

URL: http://hdl.handle.net/1853/50313

► We will discuss what is known about the construction of contact structures via branched covers, emphasizing the search for universal transverse knots. Recall that a… (more)

Subjects/Keywords: Branched covers; Contact geometry; Contact manifolds; Topology; Manifolds (Mathematics); Three-manifolds (Topology); Covering spaces (Topology)

…made to the case of contact manifolds. One such construction is branched covers. In the past… …contact structures. Our goal is to better understand branched covers of 3-manifolds and contact… …manifolds. The real substance to the subject of branched covers of contact manifolds came in 2002… …interested in contact manifolds) we want to construct open book decompositions for manifolds… …much about the behavior of the structure and for constructing contact manifolds via surgery…

2 more images…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Casey, M. P. (2013). Branched covers of contact manifolds. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/50313

Chicago Manual of Style (16^th Edition):

Casey, Meredith Perrie. “Branched covers of contact manifolds.” 2013. Doctoral Dissertation, Georgia Tech. Accessed March 08, 2021. http://hdl.handle.net/1853/50313.

MLA Handbook (7^th Edition):

Casey, Meredith Perrie. “Branched covers of contact manifolds.” 2013. Web. 08 Mar 2021.

Vancouver:

Casey MP. Branched covers of contact manifolds. [Internet] [Doctoral dissertation]. Georgia Tech; 2013. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/1853/50313.

Council of Science Editors:

Casey MP. Branched covers of contact manifolds. [Doctoral Dissertation]. Georgia Tech; 2013. Available from: http://hdl.handle.net/1853/50313

University of South Africa

17. Tshikunguila, Tshikuna-Matamba. The differential geometry of the fibres of an almost contract metric submersion .

Degree: 2013, University of South Africa

URL: http://hdl.handle.net/10500/18622

► Almost contact metric submersions constitute a class of Riemannian submersions whose total space is an almost contact metric manifold. Regarding the base space, two types… (more)

▼ Almost contact metric submersions constitute a class of Riemannian submersions whose total space is an almost contact metric manifold. Regarding the base space, two types are studied. Submersions of type I are those whose base space is an almost contact metric manifold while, when the base space is an almost Hermitian manifold, then the submersion is said to be of type II. After recalling the known notions and fundamental properties to be used in the sequel, relationships between the structure of the fibres with that of the total space are established. When the fibres are almost Hermitian manifolds, which occur in the case of a type I submersions, we determine the classes of submersions whose fibres are Kählerian, almost Kählerian, nearly Kählerian, quasi Kählerian, locally conformal (almost) Kählerian, Gi-manifolds and so on. This can be viewed as a classification of submersions of type I based upon the structure of the fibres. Concerning the fibres of a type II submersions, which are almost contact metric manifolds, we discuss how they inherit the structure of the total space. Considering the curvature property on the total space, we determine its corresponding on the fibres in the case of a type I submersions. For instance, the cosymplectic curvature property on the total space corresponds to the Kähler identity on the fibres. Similar results are obtained for Sasakian and Kenmotsu curvature properties. After producing the classes of submersions with minimal, superminimal or umbilical fibres, their impacts on the total or the base space are established. The minimality of the fibres facilitates the transference of the structure from the total to the base space. Similarly, the superminimality of the fibres facilitates the transference of the structure from the base to the total space. Also, it is shown to be a way to study the integrability of the horizontal distribution. Totally contact umbilicity of the fibres leads to the asymptotic directions on the total space. Submersions of contact CR-submanifolds of quasi-K-cosymplectic and quasi-Kenmotsu manifolds are studied. Certain distributions of the under consideration submersions induce the CR-product on the total space. Advisors/Committee Members: Batubenge, T. A (advisor), Massamba, F (advisor).

Subjects/Keywords: Differential Geometry; Riemannian submersions; Almost contact metric submersions; CR-submersions; Contact CR-submanifolds; Almost contact metric manifolds; Almost Hermitian manifolds; Riemannian curvature tensor; Holomorphic sectional curvature; Minimal fibres; Superminimal fibres; Umbilicity

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Tshikunguila, T. (2013). The differential geometry of the fibres of an almost contract metric submersion . (Doctoral Dissertation). University of South Africa. Retrieved from http://hdl.handle.net/10500/18622

Chicago Manual of Style (16^th Edition):

Tshikunguila, Tshikuna-Matamba. “The differential geometry of the fibres of an almost contract metric submersion .” 2013. Doctoral Dissertation, University of South Africa. Accessed March 08, 2021. http://hdl.handle.net/10500/18622.

MLA Handbook (7^th Edition):

Tshikunguila, Tshikuna-Matamba. “The differential geometry of the fibres of an almost contract metric submersion .” 2013. Web. 08 Mar 2021.

Vancouver:

Tshikunguila T. The differential geometry of the fibres of an almost contract metric submersion . [Internet] [Doctoral dissertation]. University of South Africa; 2013. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10500/18622.

Council of Science Editors:

Tshikunguila T. The differential geometry of the fibres of an almost contract metric submersion . [Doctoral Dissertation]. University of South Africa; 2013. Available from: http://hdl.handle.net/10500/18622

Michigan State University

18. Deng, Shangrong. Variational problems on contact manifolds.

Degree: PhD, Department of Mathematics, 1991, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:23041

Subjects/Keywords: Contact manifolds; Variational inequalities (Mathematics); Geometry, Differential

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Deng, S. (1991). Variational problems on contact manifolds. (Doctoral Dissertation). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:23041

Chicago Manual of Style (16^th Edition):

Deng, Shangrong. “Variational problems on contact manifolds.” 1991. Doctoral Dissertation, Michigan State University. Accessed March 08, 2021. http://etd.lib.msu.edu/islandora/object/etd:23041.

MLA Handbook (7^th Edition):

Deng, Shangrong. “Variational problems on contact manifolds.” 1991. Web. 08 Mar 2021.

Vancouver:

Deng S. Variational problems on contact manifolds. [Internet] [Doctoral dissertation]. Michigan State University; 1991. [cited 2021 Mar 08]. Available from: http://etd.lib.msu.edu/islandora/object/etd:23041.

Council of Science Editors:

Deng S. Variational problems on contact manifolds. [Doctoral Dissertation]. Michigan State University; 1991. Available from: http://etd.lib.msu.edu/islandora/object/etd:23041

University of New Mexico

19. Pati, Justin. Contact homology of toric contact manifolds of Reeb type.

Degree: Mathematics & Statistics, 2010, University of New Mexico

URL: http://hdl.handle.net/1928/11193

► We use contact homology to distinguish contact structures on various manifolds. We are primarily interested in contact manifolds which admit an action of Reeb type… (more)

Subjects/Keywords: Contact manifolds; Symplectic and contact topology; Toric varieties; Orbifolds; Homology theory.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Pati, J. (2010). Contact homology of toric contact manifolds of Reeb type. (Doctoral Dissertation). University of New Mexico. Retrieved from http://hdl.handle.net/1928/11193

Chicago Manual of Style (16^th Edition):

Pati, Justin. “Contact homology of toric contact manifolds of Reeb type.” 2010. Doctoral Dissertation, University of New Mexico. Accessed March 08, 2021. http://hdl.handle.net/1928/11193.

MLA Handbook (7^th Edition):

Pati, Justin. “Contact homology of toric contact manifolds of Reeb type.” 2010. Web. 08 Mar 2021.

Vancouver:

Pati J. Contact homology of toric contact manifolds of Reeb type. [Internet] [Doctoral dissertation]. University of New Mexico; 2010. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/1928/11193.

Council of Science Editors:

Pati J. Contact homology of toric contact manifolds of Reeb type. [Doctoral Dissertation]. University of New Mexico; 2010. Available from: http://hdl.handle.net/1928/11193

Indian Institute of Science

20. Kulkarni, Dheeraj. Relative Symplectic Caps, Fibered Knots And 4-Genus.

Degree: PhD, Faculty of Science, 2014, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2285

► The 4-genus of a knot in S3 is an important measure of complexity, related to the unknotting number. A fundamental result used to study the… (more)

Subjects/Keywords: Symplectic Geometry; Symplectic Capping Theorem; Symlpectic Manifolds; Fibered Knots; 4-Genus Knots; Symplectic Caps; Knot Theory; Contact Geometry; Contact Manifolds; Quasipositive Knots; Symplectic Convexity; Topology; Symplectic Neighborhood Theorem; Seifert Surfaces; Riemann Surface; Geometry

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Kulkarni, D. (2014). Relative Symplectic Caps, Fibered Knots And 4-Genus. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2285

Chicago Manual of Style (16^th Edition):

Kulkarni, Dheeraj. “Relative Symplectic Caps, Fibered Knots And 4-Genus.” 2014. Doctoral Dissertation, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/2285.

MLA Handbook (7^th Edition):

Kulkarni, Dheeraj. “Relative Symplectic Caps, Fibered Knots And 4-Genus.” 2014. Web. 08 Mar 2021.

Vancouver:

Kulkarni D. Relative Symplectic Caps, Fibered Knots And 4-Genus. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2014. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/2285.

Council of Science Editors:

Kulkarni D. Relative Symplectic Caps, Fibered Knots And 4-Genus. [Doctoral Dissertation]. Indian Institute of Science; 2014. Available from: http://etd.iisc.ac.in/handle/2005/2285

21. Μάρκελλος, Μιχαήλ. Μελέτη ειδικών κατηγοριών πολλαπλοτήτων επαφής Riemann.

Degree: 2009, University of Patras; Πανεπιστήμιο Πατρών

URL: http://hdl.handle.net/10442/hedi/18245

►

The main object of this Doctoral Thesis is the study of the geometry of 3-dimensional H-contact metric manifolds, or, equivalently, the contact metric manifolds whose… (more)

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The main object of this Doctoral Thesis is the study of the geometry of 3-dimensional H-contact metric manifolds, or, equivalently, the contact metric manifolds whose the vector field ξ is an eigenvector of the Ricci operator Q. More precisely, it is proved that 3-dimensional H-contact metric manifolds [M, (η, ξ, φ, g)] are geometrically characterized by a specific curvature condition and three differentiable functions κ, μ and ν of M. This condition leads to the introduction of a new class of contact metric manifolds: the (κ, μ, ν)-contact metric manifolds. It is remarkable that for dimension greater than three, such manifolds are reduced to (κ, μ)-contact metric manifolds, i.e. the functions κ, μ are constants and the function ν is the zero function. On the contrary, in three dimension (κ, μ, ν)-contact metric manifolds exist. Another problem which is studied is the classification of biharmonic Legendre curves and anti-invariant surfaces immersed in 3-dimensional (κ, μ, ν)-contact metric manifolds. It is proved that biharmonic Legendre curves in 3-dimensional (κ, μ, ν)-contact metric manifolds are necessarily geodesics. Furthermore, it is proved that biharmonic and without minimal points anti-invariant surfaces immersed in 3-dimensional generalized (κ, μ)-contact metric manifolds with constant norm of the mean curvature vector field, are locally flat.

Το κύριο αντικείμενο της διατριβής συνίσταται στη μελέτη της γεωμετρίας των τρισδιάστατων H-μετρικών πολλαπλοτήτων επαφής, ή, ισοδύναμα, των μετρικών πολλαπλοτήτων επαφής για τις οποίες το διανυσματικό πεδίο ξ είναι πεδίο ιδιοδιανυσμάτων του τελεστή Ricci Q. Συγκεκριμένα, αποδεικνύεται ότι μια τρισδιάστατη H-μετρική πολλαπλότητα επαφής [Μ, (η, ξ, φ, g)] χαρακτηρίζεται γεωμετρικά από μια συνθήκη που εμπλέκει τον τανυστή καμπυλότητας της Μ και τρεις διαφορίσιμες συναρτήσεις κ, μ και ν της Μ. Η συνθήκη αυτή οδηγεί στην εισαγωγή μιας νέας κλάσης μετρικών πολλαπλοτήτων επαφής: τις (κ, μ, ν)-πολλαπλότητες επαφής. Το ενδιαφέρον με τις (κ, μ, ν)-πολλαπλότητες επαφής είναι ότι για διάσταση μεγαλύτερη του τρία εκφυλίζονται στις (κ, μ)-πολλαπλότητες επαφής, δηλαδή, οι συναρτήσεις κ, μ είναι σταθερές και η συνάρτηση ν είναι η μηδενική συνάρτηση. Αντιθέτως, αποδεικνύεται ότι τέτοιες μετρικές πολλαπλότητες επαφής υπάρχουν στη διάσταση τρία. Ένα άλλο από τα προβλήματα που εξετάζονται σ' αυτή τη διατριβή είναι ο χαρακτηρισμός των διαρμονικών καμπυλών του Legendre και των αντι-αναλλοίωτων επιφανειών εμβυθισμένων σε τρισδιάστατες (κ, μ, ν)-πολλαπλότητες επαφής. Συγκεκριμένα, αποδεικνύεται ότι οι διαρμονικές καμπύλες του Legendre είναι οι γεωδαισιακές αυτών των χώρων. Επιπλέον, αποδεικνύεται ότι οι διαρμονικές και χωρίς ελαχιστικά σημεία αντι-αναλλοίωτες επιφάνειες που είναι εμβυθισμένες σε τρισδιάστατες γενικευμένες (κ, μ)-πολλαπλότητες επαφής και των οποίων το μέτρο του διανυσματικού πεδίου της μέσης καμπυλότητας είναι σταθερό, είναι τοπικά Ευκλείδειες.

Subjects/Keywords: Μετρικές πολλαπλότητες επαφής; Κ, μ, ν, μετρικές πολλαπλότητες επαφής; Αρμονικά χαρακτηριστικά διανυσματικά πεδία; Η - πολλαπλότητες επαφής; Αρμονικές απεικονίσεις; Διαρμονικές απεικονίσεις; Contact metric manifolds; Κ, μ, ν, contact metric manifolds; Harmonic characteristic vector fields; Η - contact manifolds

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Μάρκελλος, . �. (2009). Μελέτη ειδικών κατηγοριών πολλαπλοτήτων επαφής Riemann. (Thesis). University of Patras; Πανεπιστήμιο Πατρών. Retrieved from http://hdl.handle.net/10442/hedi/18245

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Μάρκελλος, Μιχαήλ. “Μελέτη ειδικών κατηγοριών πολλαπλοτήτων επαφής Riemann.” 2009. Thesis, University of Patras; Πανεπιστήμιο Πατρών. Accessed March 08, 2021. http://hdl.handle.net/10442/hedi/18245.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Μάρκελλος, Μιχαήλ. “Μελέτη ειδικών κατηγοριών πολλαπλοτήτων επαφής Riemann.” 2009. Web. 08 Mar 2021.

Vancouver:

Μάρκελλος �. Μελέτη ειδικών κατηγοριών πολλαπλοτήτων επαφής Riemann. [Internet] [Thesis]. University of Patras; Πανεπιστήμιο Πατρών; 2009. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10442/hedi/18245.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Μάρκελλος �. Μελέτη ειδικών κατηγοριών πολλαπλοτήτων επαφής Riemann. [Thesis]. University of Patras; Πανεπιστήμιο Πατρών; 2009. Available from: http://hdl.handle.net/10442/hedi/18245

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

22. Silva, André Vanderlinde da. Sobre fluxos de Reeb tri-dimensionais: existência implicada de órbitas periódicas e uma caracterização dinâmica do toro sólido.

Degree: PhD, Matemática, 2014, University of São Paulo

URL: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05022015-222314/ ;

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Neste trabalho, estudamos a dinâmica de Reeb associada a uma forma de contato \λ definida numa 3-variedade compacta e conexa M. Assumimos que \λ é… (more)

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Neste trabalho, estudamos a dinâmica de Reeb associada a uma forma de contato \λ definida numa 3-variedade compacta e conexa M. Assumimos que \λ é tight e a primeira classe de Chern da estrutura de contato \ξ=\\ker\λ se anula sobre \π₂(M). No nosso primeiro resultado, supomos que M é fechada e existe uma órbita fechada L do fluxo de Reeb que é um p-nó trivial com número de auto-enlaçamento -1/p. Supomos, além disso, que o número de rotação transversal da p-ésima iterada de L é estritamente menor do que 1. Nestas condições, provamos que existe uma órbita fechada (de Reeb) contrátil geometricamente distinta de L e não-enlaçada em L cujo número de rotação transversal é 1. Apresentamos também uma versão deste resultado para o caso em que M é uma 3-variedade cujo bordo é difeomorfo a um toro e invariante pelo fluxo de Reeb e não existem órbitas fechadas contidas no bordo. Nosso segundo resultado é uma caracterização dinâmica do toro sólido. Seja \λ uma forma de contato não-degenerada definida em uma 3-variedade M cujo bordo é difeomorfo a um toro e invariante pelo fluxo de Reeb. Se o fluxo de Reeb satisfaz certas hipóteses de torção sobre o bordo, então ou existe uma órbita fechada contrátil com índice de Conley-Zehnder 2 ou M é folheada por discos transversais ao campo de Reeb. Neste último caso, M é difeomorfa a um toro sólido e existe uma órbita fechada não-contrátil em M que é ponto fixo da aplicação de retorno induzida pela folheação.

In this work, we study the Reeb dynamics associated to a tight contact form \λ defined on a compact, connected 3-manifold M. Suppose that the first Chern class of \ξ=\\ker\λ vanish on \π₂(M). In our first result, we assume that M is closed and there exists a closed Reeb orbit L which is a p-unknotted, has self-linking number -1/p and the transverse rotation number of the p-th iterate of L is less than 1. Under these conditions, we verify that there exists a contractible closed Reeb orbit which is geometrically distinct from L and not linked to L with transverse rotation number 1. We also prove a version of this result when M is a compact 3-manifold M whose boundary is diffeomorphic to a torus and invariant by the flow and, moreover, there does not exist closed Reeb orbits on the boundary. Our second result is a dynamical characterization of the solid torus. We assume that \λ is a contact form on a compact 3-manifold M whose boundary is diffeomorphic to a torus. Under the hypothesis of \λ being non-degenerate, if the flow is tangent to \\partial M and satisfies some twist conditions on the boundary, then either there exists a contractible closed Reeb orbit which has Conley-Zehnder index 2 or M is foliated by disks transverse to the Reeb flow. In this last case, we see that M is diffeomorphic to a solid torus and there exists a non-contractible closed Reeb orbit M which is a fixed point of the return map induced by the foliation.

Advisors/Committee Members: Hryniewicz, Umberto Leone, Salomão, Pedro Antonio Santoro.

Subjects/Keywords: Closed orbits; Contact manifolds; Curvas pseudo-holomorfas em simplectizações; Dinâmica de Reeb; Folheações transversais; Órbitas periódicas; Pseudo-holomorphic curves in simplectizations; Reeb dynamics; Transverse foliations.; Variedades de contato

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Silva, A. V. d. (2014). Sobre fluxos de Reeb tri-dimensionais: existência implicada de órbitas periódicas e uma caracterização dinâmica do toro sólido. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05022015-222314/ ;

Chicago Manual of Style (16^th Edition):

Silva, André Vanderlinde da. “Sobre fluxos de Reeb tri-dimensionais: existência implicada de órbitas periódicas e uma caracterização dinâmica do toro sólido.” 2014. Doctoral Dissertation, University of São Paulo. Accessed March 08, 2021. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05022015-222314/ ;.

MLA Handbook (7^th Edition):

Silva, André Vanderlinde da. “Sobre fluxos de Reeb tri-dimensionais: existência implicada de órbitas periódicas e uma caracterização dinâmica do toro sólido.” 2014. Web. 08 Mar 2021.

Vancouver:

Silva AVd. Sobre fluxos de Reeb tri-dimensionais: existência implicada de órbitas periódicas e uma caracterização dinâmica do toro sólido. [Internet] [Doctoral dissertation]. University of São Paulo; 2014. [cited 2021 Mar 08]. Available from: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05022015-222314/ ;.

Council of Science Editors:

Silva AVd. Sobre fluxos de Reeb tri-dimensionais: existência implicada de órbitas periódicas e uma caracterização dinâmica do toro sólido. [Doctoral Dissertation]. University of São Paulo; 2014. Available from: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05022015-222314/ ;

University of Michigan

23. Boland, Jeffrey Ronald. The dynamics and geometry of contact Anosov flows.

Degree: PhD, Pure Sciences, 1998, University of Michigan

URL: http://hdl.handle.net/2027.42/131167

► We study the rigidity of negatively curved Riemannian manifolds from the dynamical point of view by considering contact Anosov flows on their unit tangent bundles.… (more)

Subjects/Keywords: Contact Anosov Flows; Dynamics; Finsler Geometry; Geodesic Flows; Riemannian Manifolds

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Boland, J. R. (1998). The dynamics and geometry of contact Anosov flows. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/131167

Chicago Manual of Style (16^th Edition):

Boland, Jeffrey Ronald. “The dynamics and geometry of contact Anosov flows.” 1998. Doctoral Dissertation, University of Michigan. Accessed March 08, 2021. http://hdl.handle.net/2027.42/131167.

MLA Handbook (7^th Edition):

Boland, Jeffrey Ronald. “The dynamics and geometry of contact Anosov flows.” 1998. Web. 08 Mar 2021.

Vancouver:

Boland JR. The dynamics and geometry of contact Anosov flows. [Internet] [Doctoral dissertation]. University of Michigan; 1998. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/2027.42/131167.

Council of Science Editors:

Boland JR. The dynamics and geometry of contact Anosov flows. [Doctoral Dissertation]. University of Michigan; 1998. Available from: http://hdl.handle.net/2027.42/131167

Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)

24. Θεοφανίδης, Θεοχάρης. Μελέτη πραγματικών υπερεπιφανειών μη ευκλείδειων μιγαδικών χώρων μορφής.

Degree: 2011, Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)

URL: http://hdl.handle.net/10442/hedi/27049

► J. de Dios Perez, F. G. Santos and Y. J. Suh in [29], studied real hypersurfaces of dimension greater than 3 in complex projective spaces,… (more)

Subjects/Keywords: Διαφορική γεωμετρία; Πολλαπλότητα Riemann; Μιγαδικός χώρος μορφής; Πραγματική υπερεπιφάνεια; Δομή σχεδόν επαφής; Τελεστής δομής Jacobi; Differential geometry; Riemannian manifolds; Complex space form; Real hypersurface; Almost contact structure; Jacobi structure operator

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Θεοφανίδης, . �. (2011). Μελέτη πραγματικών υπερεπιφανειών μη ευκλείδειων μιγαδικών χώρων μορφής. (Thesis). Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ). Retrieved from http://hdl.handle.net/10442/hedi/27049

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Θεοφανίδης, Θεοχάρης. “Μελέτη πραγματικών υπερεπιφανειών μη ευκλείδειων μιγαδικών χώρων μορφής.” 2011. Thesis, Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ). Accessed March 08, 2021. http://hdl.handle.net/10442/hedi/27049.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Θεοφανίδης, Θεοχάρης. “Μελέτη πραγματικών υπερεπιφανειών μη ευκλείδειων μιγαδικών χώρων μορφής.” 2011. Web. 08 Mar 2021.

Vancouver:

Θεοφανίδης �. Μελέτη πραγματικών υπερεπιφανειών μη ευκλείδειων μιγαδικών χώρων μορφής. [Internet] [Thesis]. Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); 2011. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10442/hedi/27049.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Θεοφανίδης �. Μελέτη πραγματικών υπερεπιφανειών μη ευκλείδειων μιγαδικών χώρων μορφής. [Thesis]. Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); 2011. Available from: http://hdl.handle.net/10442/hedi/27049

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)

25. Μουτάφη, Ευαγγελία. Μελέτη πολλαπλοτήτων επαφής με τη βοήθεια καμπυλοτήτων.

Degree: 2010, Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)

URL: http://hdl.handle.net/10442/hedi/22094

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The aim of this thesis which is entitled “Study of Contact Manifolds Using the Curvature”, is the study of 3-dimensional contact metric manifolds which are… (more)

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The aim of this thesis which is entitled “Study of Contact Manifolds Using the Curvature”, is the study of 3-dimensional contact metric manifolds which are also pseudosymmetric according to R. Deszcz. Firstly, we generalize the results of J. T. Cho and J. Inoguchi for pseudosymmetric contact 3-manifolds which satisfy the condition Qφ = φQ. Next, we prove the necessary and sufficient conditions for a 3-dimensional contact metric manifold to be a pseudosymmetric manifold. Finally, we use these conditions to study and classify the 3-dimensional contact metric manifolds which satisfy one of the following conditions: 1) M is a 3 – τ contact manifold which is pseudosymmetric, 2) M is a 3 – τ – α contact manifold which is pseudosymmetric of constant type, where a is a smooth function on M, 3) M is pseudosymmetric with Qξ = ρξ, where ρ is a smooth function on M which is constant along the direction of ξ, 4) M is pseudosymmetric of constant type with Qξ = ρξ, where ρ is a smooth function on M, 5) M is a (κ, μ, ν) - contact metric pseudosymmetric manifold of type constant in the direction of ξ and 6) M is a pseudosymmetric contact metric manifold with harmonic curvature and Trl is constant along the direction of ξ.

Σκοπός αυτής της διατριβής που έχει τίτλο «Μελέτη Πολλαπλοτήτων Επαφής με τη Βοήθεια Καμπυλοτήτων», είναι η μελέτη των ψευδοσυμμετρικών (σύμφωνα με τον ορισμό του R. Deszcz) πολλαπλοτήτων επαφής στη διάσταση τρία. Αρχικά, γενικεύεται ένα Θεώρημα των J. T. Cho – J. Inoguchi για τις ψευδοσυμμετρικές πολλαπλότητες επαφής με την ιδιότητα Qφ = φQ. Στη συνέχεια, διατυπώνονται και αποδεικνύονται οι ικανές και αναγκαίες συνθήκες, ώστε μία τρισδιάστατη μετρική πολλαπλότητα επαφής να είναι ψευδοσυμμετρική. Τέλος, χρησιμοποιώντας τις συνθήκες αυτές μελετώνται και ταξινομούνται οι τρισδιάστατες μετρικές πολλαπλότητες επαφής Μ που ικανοποιούν μία από τις παρακάτω συνθήκες: 1) η M είναι 3 – τ και ψευδοσυμμετρική, 2) η M είναι 3 – τ – α και ψευδοσυμμετρική σταθερού τύπου, όπου α είναι λεία συνάρτηση στη M, 3) η M είναι ψευδοσυμμετρική με την ιδιότητα Qξ = ρξ, όπου ρ είναι λεία συνάρτηση στη M σταθερή κατά τη διεύθυνση του ξ, 4) η M είναι ψευδοσυμμετρική σταθερού τύπου με την ιδιότητα Qξ = ρξ, όπου ρ είναι λεία συνάρτηση στη Μ, 5) η M είναι μία ψευδοσυμμετρική (κ, μ, ν) – πολλαπλότητα επαφής τύπου σταθερού κατά τη διεύθυνση του ξ και 6) η M είναι ψευδοσυμμετρική μετρική πολλαπλότητα επαφής με αρμονική καμπυλότητα και Trl σταθερό κατά τη διεύθυνση του ξ.

Subjects/Keywords: Επαφής μετρικές πολλαπλότητες; Ψευδοσυμμετρικοί χώροι κατά R. Deszcz; Contact metric manifolds; Pseudosymmetric spaces according to R. Deszcz

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Μουτάφη, . �. (2010). Μελέτη πολλαπλοτήτων επαφής με τη βοήθεια καμπυλοτήτων. (Thesis). Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ). Retrieved from http://hdl.handle.net/10442/hedi/22094

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Μουτάφη, Ευαγγελία. “Μελέτη πολλαπλοτήτων επαφής με τη βοήθεια καμπυλοτήτων.” 2010. Thesis, Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ). Accessed March 08, 2021. http://hdl.handle.net/10442/hedi/22094.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Μουτάφη, Ευαγγελία. “Μελέτη πολλαπλοτήτων επαφής με τη βοήθεια καμπυλοτήτων.” 2010. Web. 08 Mar 2021.

Vancouver:

Μουτάφη �. Μελέτη πολλαπλοτήτων επαφής με τη βοήθεια καμπυλοτήτων. [Internet] [Thesis]. Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); 2010. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10442/hedi/22094.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Μουτάφη �. Μελέτη πολλαπλοτήτων επαφής με τη βοήθεια καμπυλοτήτων. [Thesis]. Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); 2010. Available from: http://hdl.handle.net/10442/hedi/22094

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

26. JosÃ Nazareno Vieira Gomes. Rigidez de superfÃcies de contato e caracterizaÃÃo de variedades riemannianas munidas de um campo conforme ou de alguma mÃtrica especial.

Degree: PhD, 2012, Universidade Federal do Ceará

URL: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=8660 ;

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Esta tese estÃ composta de quatro partes distintas. Na primeira parte, vamos dar uma nova caracterizaÃÃo da esfera euclidiana como a Ãnica variedade Riemanniana compacta… (more)

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Esta tese estÃ composta de quatro partes distintas. Na primeira parte, vamos dar uma nova caracterizaÃÃo da esfera euclidiana como a Ãnica variedade Riemanniana compacta com curvatura escalar constante e admitindo um campo de vetores conforme nÃo trivial que Ã tambÃm Ricci conforme. Na segunda parte, provaremos algumas propriedades dos quase sÃlitons de Ricci, as quais permitem estabelecer condiÃÃes de rigidez desses objetos, bem como caracterizar as estruturas de quase sÃlitons de Ricci gradiente na esfera euclidiana. ImersÃes isomÃtricas tambÃm serÃo consideradas; classificaremos os quase sÃlitons de Ricci imersos em formas espaciais, atravÃs de uma condiÃÃo algÃbrica sobre a funÃÃo sÃliton. AlÃm disso, vamos caracterizar, atravÃs de uma condiÃÃo sobre o operador de umbilicidade, as hipersuperfÃcies n-dimensionais de uma forma espacial, com curvatura mÃdia constante, tendo duas curvaturas principais distintas e com multiplicidades p e n - p. Na terceira parte, provaremos um resultado de rigidez e algumas fÃrmulas integrais para uma mÃtrica m-quasi-Einstein generalizada compacta. Na Ãltima parte, vamos apresentar uma relaÃÃo entre a curvatura gaussiana e o Ãngulo de contato de superfÃcies imersas na esfera euclidiana tridimensional,a qual permite concluir que a superfÃcie Ã plana, se o Ãngulo de contato for constante. AlÃm disso, deduziremos que o toro de Clifford Ã a Ãnica superfÃcie compacta com curvatura mÃdia constante tendo tal propriedade.

This thesis is composed of four distinct parts. In the first part, we shall give a new characterization of the Euclidean sphere as the only compact Riemannian manifold with constant scalar curvature carrying a conformal vector eld non-trivial which is also Ricci conformal. In the second part, we shall prove some properties of almost Ricci solitons, which allow us to establish conditions for rigidity of these objects, as well as characterize the structures of gradient almost Ricci soliton in Euclidean sphere. Isometric immersions also will be considered, we shall classify almost Ricci solitons immersed in space forms, through algebraic condition on soliton function. Furthermore, we characterize under a condition of the umbilicity operator, n-dimensional hypersurfaces in a space form with constant mean curvature, admitting two distinct principal curvatures with multiplicities p and n - p. In the third part, we prove a result of rigidity and some integral formulae for a compact generalized m-quasi-Einstein metric. In the last part, we present a relation between the Gaussian curvature and the contact angle of surfaces immersed in Euclidean three-dimensional sphere, which allows us to conclude that such a surface is at provided its contact angle is constant. Moreover, we deduce that Clifford tori are the unique compact surfaces with constant mean curvature having such property.

Advisors/Committee Members: Gregorio Pacelli Feitosa Bessa, AbdÃnago Alves de Barros, Renato de Azevedo Tribuzy, Ernani de Sousa Ribeiro Junior, Francesco Mercuri.

Subjects/Keywords: GEOMETRIA DIFERENCIAL; Ãngulo de contato; toro de Clifford; curvatura mÃdia constante; esfera euclidiana; quase sÃliton de Ricci; campo de vetores conforme; curvatura escalar constante; contact angle; Clifford torus; constant mean curvature; euclidian sphere; almost Ricci soliton; conformal vector fields; constant scalar curvature; variedades riemanianas; Riemannian manifolds

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APA (6^th Edition):

Gomes, J. N. V. (2012). Rigidez de superfÃcies de contato e caracterizaÃÃo de variedades riemannianas munidas de um campo conforme ou de alguma mÃtrica especial. (Doctoral Dissertation). Universidade Federal do Ceará. Retrieved from http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=8660 ;

Chicago Manual of Style (16^th Edition):

Gomes, JosÃ Nazareno Vieira. “Rigidez de superfÃcies de contato e caracterizaÃÃo de variedades riemannianas munidas de um campo conforme ou de alguma mÃtrica especial.” 2012. Doctoral Dissertation, Universidade Federal do Ceará. Accessed March 08, 2021. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=8660 ;.

MLA Handbook (7^th Edition):

Gomes, JosÃ Nazareno Vieira. “Rigidez de superfÃcies de contato e caracterizaÃÃo de variedades riemannianas munidas de um campo conforme ou de alguma mÃtrica especial.” 2012. Web. 08 Mar 2021.

Vancouver:

Gomes JNV. Rigidez de superfÃcies de contato e caracterizaÃÃo de variedades riemannianas munidas de um campo conforme ou de alguma mÃtrica especial. [Internet] [Doctoral dissertation]. Universidade Federal do Ceará 2012. [cited 2021 Mar 08]. Available from: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=8660 ;.

Council of Science Editors:

Gomes JNV. Rigidez de superfÃcies de contato e caracterizaÃÃo de variedades riemannianas munidas de um campo conforme ou de alguma mÃtrica especial. [Doctoral Dissertation]. Universidade Federal do Ceará 2012. Available from: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=8660 ;

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