subject:(special manifolds)

University of Oxford

1. Clancy, Robert. Spin(7)-manifolds and calibrated geometry.

Degree: PhD, 2012, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:c37748b3-674a-4d95-8abf-7499474abce3 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581050

► In this thesis we study Spin(7)-manifolds, that is Riemannian 8-manifolds with torsion-free Spin(7)-structures, and Cayley submanifolds of such manifolds. We use a construction of compact… (more)

Subjects/Keywords: 539.725; Differential geometry; Geometry; spin(7)-manifolds; special holonomy; Cayley submanifolds

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APA (6^th Edition):

Clancy, R. (2012). Spin(7)-manifolds and calibrated geometry. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:c37748b3-674a-4d95-8abf-7499474abce3 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581050

Chicago Manual of Style (16^th Edition):

Clancy, Robert. “Spin(7)-manifolds and calibrated geometry.” 2012. Doctoral Dissertation, University of Oxford. Accessed February 26, 2021. http://ora.ox.ac.uk/objects/uuid:c37748b3-674a-4d95-8abf-7499474abce3 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581050.

MLA Handbook (7^th Edition):

Clancy, Robert. “Spin(7)-manifolds and calibrated geometry.” 2012. Web. 26 Feb 2021.

Vancouver:

Clancy R. Spin(7)-manifolds and calibrated geometry. [Internet] [Doctoral dissertation]. University of Oxford; 2012. [cited 2021 Feb 26]. Available from: http://ora.ox.ac.uk/objects/uuid:c37748b3-674a-4d95-8abf-7499474abce3 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581050.

Council of Science Editors:

Clancy R. Spin(7)-manifolds and calibrated geometry. [Doctoral Dissertation]. University of Oxford; 2012. Available from: http://ora.ox.ac.uk/objects/uuid:c37748b3-674a-4d95-8abf-7499474abce3 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581050

University of Western Ontario

2. Rosario-Ortega, Josue. Moduli space and deformations of special Lagrangian submanifolds with edge singularities.

Degree: 2016, University of Western Ontario

URL: https://ir.lib.uwo.ca/etd/3924

► Special Lagrangian submanifolds are submanifolds of a Calabi-Yau manifold calibrated by the real part of the holomorphic volume form. In this thesis we use elliptic… (more)

Subjects/Keywords: singular manifolds; special Lagrangian submanifolds; edge-degenerate differential operators; boundary value problems; moduli spaces; Analysis; Geometry and Topology

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APA (6^th Edition):

Rosario-Ortega, J. (2016). Moduli space and deformations of special Lagrangian submanifolds with edge singularities. (Thesis). University of Western Ontario. Retrieved from https://ir.lib.uwo.ca/etd/3924

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):

Rosario-Ortega, Josue. “Moduli space and deformations of special Lagrangian submanifolds with edge singularities.” 2016. Thesis, University of Western Ontario. Accessed February 26, 2021. https://ir.lib.uwo.ca/etd/3924.

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

MLA Handbook (7^th Edition):

Rosario-Ortega, Josue. “Moduli space and deformations of special Lagrangian submanifolds with edge singularities.” 2016. Web. 26 Feb 2021.

Vancouver:

Rosario-Ortega J. Moduli space and deformations of special Lagrangian submanifolds with edge singularities. [Internet] [Thesis]. University of Western Ontario; 2016. [cited 2021 Feb 26]. Available from: https://ir.lib.uwo.ca/etd/3924.

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

Council of Science Editors:

Rosario-Ortega J. Moduli space and deformations of special Lagrangian submanifolds with edge singularities. [Thesis]. University of Western Ontario; 2016. Available from: https://ir.lib.uwo.ca/etd/3924

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

Colorado State University

3. Lui, Yui Man. Geometric methods on special manifolds for visual recognition.

Degree: PhD, Computer Science, 2010, Colorado State University

URL: http://hdl.handle.net/10217/39042

► Many computer vision methods assume that the underlying geometry of images is Euclidean. This assumption is generally not valid. Therefore, this dissertation introduces new nonlinear… (more)

▼ Many computer vision methods assume that the underlying geometry of images is Euclidean. This assumption is generally not valid. Therefore, this dissertation introduces new nonlinear geometric frameworks based upon special manifolds, namely Graβmann and Stiefel manifolds, for visual recognition. The motivation for this thesis is driven by the intrinsic geometry of visual data in which the visual data can be either a still image or video. Visual data are represented as points in appropriately chosen parameter spaces. The idiosyncratic aspects of the data in these spaces are then exploited for pattern classification. Three major research results are presented in this dissertation: face recognition for illumination spaces on Stiefel manifolds, face recognition on Graβmann registration manifolds, and action classification on product manifolds. Previous work has shown that illumination cones are idiosyncratic for face recognition in illumination spaces. However, it has not been addressed how a single image relates to an illumination cone. In this dissertation, a Bayesian model is employed to relight a single image to a set of illuminated variants. The subspace formed by these illuminated variants is characterized on a Stiefel manifold. A new distance measure called Canonical Stiefel Quotient (CSQ) is introduced. CSQ performs two projections on a tangent space of a Stiefel manifold and uses the quotient for classification. The proposed method demonstrates that illumination cones can be synthesized by relighting a single image to a set of images, and the synthesized illumination cones are discriminative for face recognition. Experiments on the CMU-PIE and YaleB data sets reveal that CSQ not only achieves high recognition accuracies for generic faces but also is robust to the choice of training sets. Subspaces can be realized as points on Graβmann manifolds. Motivated by image perturbation and the geometry of Graβmann manifolds, we present a method called Graβmann Registration Manifolds (GRM) for face recognition. First, a tangent space is formed by a set of affine perturbed images where the tangent space admits a vector space structure. Second, the tangent spaces are embedded on a Graβmann manifold and chordal distance is used to compare subspaces. Experiments on the FERET database suggest that the proposed method yields excellent results using both holistic and local features. Specifically, on the FERET Dup2 data set, which is generally considered the most difficult data set on FERET, the proposed method achieves the highest rank one identification rate among all non-trained methods currently in the literature. Human actions compose a series of movements and can be described by a sequence of video frames. Since videos are multidimensional data, data tensors are the natural choice for data representation. In this dissertation, a data tensor is expressed as a point on a product manifold and classification is performed on this product space. First, we factorize a data tensor using a modified High Order Singular Value… Advisors/Committee Members: Beveridge, J. Ross (advisor), Kirby, Michael, 1961- (committee member), Draper, Bruce A. (Bruce Austin), 1962- (committee member), Whitley, L. Darrell (committee member).

Subjects/Keywords: action classification; visual recognition; special manifolds; geometric methods; face recognition; Human face recognition (Computer science); Grassmann manifolds; Stiefel manifolds

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

APA (6^th Edition):

Lui, Y. M. (2010). Geometric methods on special manifolds for visual recognition. (Doctoral Dissertation). Colorado State University. Retrieved from http://hdl.handle.net/10217/39042

Chicago Manual of Style (16^th Edition):

Lui, Yui Man. “Geometric methods on special manifolds for visual recognition.” 2010. Doctoral Dissertation, Colorado State University. Accessed February 26, 2021. http://hdl.handle.net/10217/39042.

MLA Handbook (7^th Edition):

Lui, Yui Man. “Geometric methods on special manifolds for visual recognition.” 2010. Web. 26 Feb 2021.

Vancouver:

Lui YM. Geometric methods on special manifolds for visual recognition. [Internet] [Doctoral dissertation]. Colorado State University; 2010. [cited 2021 Feb 26]. Available from: http://hdl.handle.net/10217/39042.

Council of Science Editors:

Lui YM. Geometric methods on special manifolds for visual recognition. [Doctoral Dissertation]. Colorado State University; 2010. Available from: http://hdl.handle.net/10217/39042

4. Leijon, Rasmus. On the geometry of calibrated manifolds : with applications to electrodynamics.

Degree: Mathematics and Mathematical Statistics, 2013, Umeå University

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-80675

► In this master thesis we study calibrated geometries, a family of Riemannian or Hermitian manifolds with an associated differential form, φ. We show that… (more)

Subjects/Keywords: Calibrations; geometry; plurisubharmonic functions; special Lagrangian; electrodynamics; manifolds.

…manifolds. Calibrated manifolds, or special cases thereof, will in general be the setting used… …understanding of differential geometry, complex manifolds, the calculus of several complex variables… …calibration and the special Lagrangian calibration are presented along with some theory developed by… …Introduction to manifolds. We start by defining three concepts: embeddings, submanifolds and… …submanifolds is often left out. In general we require all manifolds and submanifolds to be orientable…

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

APA (6^th Edition):

Leijon, R. (2013). On the geometry of calibrated manifolds : with applications to electrodynamics. (Thesis). Umeå University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-80675

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):

Leijon, Rasmus. “On the geometry of calibrated manifolds : with applications to electrodynamics.” 2013. Thesis, Umeå University. Accessed February 26, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-80675.

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

MLA Handbook (7^th Edition):

Leijon, Rasmus. “On the geometry of calibrated manifolds : with applications to electrodynamics.” 2013. Web. 26 Feb 2021.

Vancouver:

Leijon R. On the geometry of calibrated manifolds : with applications to electrodynamics. [Internet] [Thesis]. Umeå University; 2013. [cited 2021 Feb 26]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-80675.

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

Council of Science Editors:

Leijon R. On the geometry of calibrated manifolds : with applications to electrodynamics. [Thesis]. Umeå University; 2013. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-80675

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

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