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

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

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

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, whose Jacobi structure operator is of Codazzi type. In chapter 2 we study real hypersurfaces under the same condition, fulfilling the case of hyperbolic spaces of dimension n > 3 as long as the case of 3dimensional hypersurfaces. M. Ortega, J. de Dios Perez and F. G. Santos in [24] studied real hypersurfaces of dimension greater than 3, in complex space forms, whose Jacobi structure operator is parallel. J. de Dios Perez and F. G.Santos in [27] studied real hypersurfaces of dimension greater than 3 with recurrent structure Jacobi operator. In chapter 3 we improve [27] in dimension 3, by studying real hypersurfaces with D recurrent structure Jacobi operator, in complex planes. Furthermore we improve [24] by studying real hypersurfaces of dimension n > 3 with recurrent structure Jacobi operator. J. T. Cho and U H. Ki in [13] classified real hypersurfaces of dimension greater than 3, in complex projective spaces, which satisfy the conditions l = l and lA = Al everywhere in the real hypersurface M. In chapter 4 we improve the previous paper by classifying real hypersurfaces in complex space forms of dimension 2n (n 2) satisfying the condition l = l in D and the condition lA = Al either in D or in D?. Moreover we classify real hypersurfaces in complex space forms of dimension 2n (n 2) satisfying the condition l = l in D and the condition (r l) = , 2 C1 either in D or in D?.

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 (6th 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 (16th Edition):

Θεοφανίδης, Θεοχάρης. “Μελέτη πραγματικών υπερεπιφανειών μη ευκλείδειων μιγαδικών χώρων μορφής.” 2011. Thesis, Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ). Accessed October 28, 2020. 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 (7th Edition):

Θεοφανίδης, Θεοχάρης. “Μελέτη πραγματικών υπερεπιφανειών μη ευκλείδειων μιγαδικών χώρων μορφής.” 2011. Web. 28 Oct 2020.

Vancouver:

Θεοφανίδης . Μελέτη πραγματικών υπερεπιφανειών μη ευκλείδειων μιγαδικών χώρων μορφής. [Internet] [Thesis]. Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); 2011. [cited 2020 Oct 28]. 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


University of Oxford

2. Rubio, Roberto. Generalized geometry of type Bn.

Degree: PhD, 2014, University of Oxford

Generalized geometry of type Bn is the study of geometric structures in T+T<sup>*</sup>+1, the sum of the tangent and cotangent bundles of a manifold and a trivial rank 1 bundle. The symmetries of this theory include, apart from B-fields, the novel A-fields. The relation between Bn-geometry and usual generalized geometry is stated via generalized reduction. We show that it is possible to twist T+T<sup>*</sup>+1 by choosing a closed 2-form F and a 3-form H such that dH+F2=0. This motivates the definition of an odd exact Courant algebroid. When twisting, the differential on forms gets twisted by d+Fτ+H. We compute the cohomology of this differential, give some examples, and state its relation with T-duality when F is integral. We define Bn-generalized complex structures (Bn-gcs), which exist both in even and odd dimensional manifolds. We show that complex, symplectic, cosymplectic and normal almost contact structures are examples of Bn-gcs. A Bn-gcs is equivalent to a decomposition (T+T<sup>*</sup>+1)<sub>ℂ</sub>= L + L + U. We show that there is a differential operator on the exterior bundle of L+U, which turns L+U into a Lie algebroid by considering the derived bracket. We state and prove the Maurer-Cartan equation for a Bn-gcs. We then work on surfaces. By the irreducibility of the spinor representations for signature (n+1,n), there is no distinction between even and odd Bn-gcs, so the type change phenomenon already occurs on surfaces. We deal with normal forms and L+U-cohomology. We finish by defining G22-structures on 3-manifolds, a structure with no analogue in usual generalized geometry. We prove an analogue of the Moser argument and describe the cone of G22-structures in cohomology.

Subjects/Keywords: 516; Mathematics; 3-manifold; almost contact geometry; complex geometry; deformation theory; G2(2)-structure; generalized complex geometry; twisted cohomology; generalized geometry; Lie algebroid

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

APA (6th Edition):

Rubio, R. (2014). Generalized geometry of type Bn. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:e0e48bb4-ea5c-4686-8b91-fcec432eb89a ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.669803

Chicago Manual of Style (16th Edition):

Rubio, Roberto. “Generalized geometry of type Bn.” 2014. Doctoral Dissertation, University of Oxford. Accessed October 28, 2020. http://ora.ox.ac.uk/objects/uuid:e0e48bb4-ea5c-4686-8b91-fcec432eb89a ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.669803.

MLA Handbook (7th Edition):

Rubio, Roberto. “Generalized geometry of type Bn.” 2014. Web. 28 Oct 2020.

Vancouver:

Rubio R. Generalized geometry of type Bn. [Internet] [Doctoral dissertation]. University of Oxford; 2014. [cited 2020 Oct 28]. Available from: http://ora.ox.ac.uk/objects/uuid:e0e48bb4-ea5c-4686-8b91-fcec432eb89a ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.669803.

Council of Science Editors:

Rubio R. Generalized geometry of type Bn. [Doctoral Dissertation]. University of Oxford; 2014. Available from: http://ora.ox.ac.uk/objects/uuid:e0e48bb4-ea5c-4686-8b91-fcec432eb89a ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.669803

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