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You searched for +publisher:"University of Notre Dame" +contributor:("Karsten Grove, Committee Chair"). Showing records 1 – 3 of 3 total matches.

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University of Notre Dame

1. Xiaoyang Chen. Curvature and Riemannian Submersions</h1>.

Degree: Mathematics, 2014, University of Notre Dame

We study Riemannian submersions from positively curved manifolds and from Einstein manifolds. We first prove a diameter rigidity theorem for Riemannian submersions.Secondly we show that there is no nontrivial Riemannian submersion from positively curved four manifolds such that either the mean curvature vector field or the norm of the O'Neill tensor is basic. We also classify Riemannian submersions from compact four-dimensional Einstein manifolds with totally geodesic fibers. Advisors/Committee Members: Karsten Grove, Committee Chair, Stephan Stolz, Committee Member, Fred Xavier, Committee Member, Xiaobo Liu, Committee Member.

Subjects/Keywords: Fred Wilhelm’s conjecture; Riemannian submersions

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

APA (6th Edition):

Chen, X. (2014). Curvature and Riemannian Submersions</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/fb494744f2q

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):

Chen, Xiaoyang. “Curvature and Riemannian Submersions</h1>.” 2014. Thesis, University of Notre Dame. Accessed December 01, 2020. https://curate.nd.edu/show/fb494744f2q.

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

MLA Handbook (7th Edition):

Chen, Xiaoyang. “Curvature and Riemannian Submersions</h1>.” 2014. Web. 01 Dec 2020.

Vancouver:

Chen X. Curvature and Riemannian Submersions</h1>. [Internet] [Thesis]. University of Notre Dame; 2014. [cited 2020 Dec 01]. Available from: https://curate.nd.edu/show/fb494744f2q.

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

Council of Science Editors:

Chen X. Curvature and Riemannian Submersions</h1>. [Thesis]. University of Notre Dame; 2014. Available from: https://curate.nd.edu/show/fb494744f2q

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


University of Notre Dame

2. John Harvey. Around Palais' Covering Homotopy Theorem</h1>.

Degree: Mathematics, 2014, University of Notre Dame

The classification by Palais of G-spaces, topological spaces acted on by homeomorphisms by a compact Lie group G, is refined. Under mild topological hypotheses, it is shown that when a sequence of orbit spaces is “close” to a limit orbit space, in some suitable sense, within a larger ambient orbit space, the G-spaces in the tail of the sequence are strongly equivalent to the limit G-space. Three applications of the theory to Alexandrov and Riemannian geometry are then given. The Covering Homotopy Theorem, which is key to the classification theory, is used to prove a version of the Slice Theorem for Alexandrov spaces, showing that the local action of a group of isometries is topologically determined by its infinitesimal action. The refinement of the classification theory is used to prove an equivariant version of Perelman’s Stability Theorem for equicontinous sequences of isometric actions by a fixed compact Lie group. The class of Riemannian orbifolds of a given dimension defined by a lower bound on the sectional curvature and the volume and an upper bound on the diameter is shown to be finite up to orbifold homeomorphism. Furthermore, any class of isospectral Riemannian orbifolds with a lower bound on the sectional curvature is also shown to be finite up to orbifold homeomorphism. Advisors/Committee Members: Xiaobo Liu, Committee Member, William Dwyer, Committee Member, Stephan Stolz, Committee Member, Karsten Grove, Committee Chair.

Subjects/Keywords: isometric actions; covering sequence theorem; alexandrov geometry; curvature bounds; isospectral orbifolds; transformation groups

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

APA (6th Edition):

Harvey, J. (2014). Around Palais' Covering Homotopy Theorem</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/qn59q239w65

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):

Harvey, John. “Around Palais' Covering Homotopy Theorem</h1>.” 2014. Thesis, University of Notre Dame. Accessed December 01, 2020. https://curate.nd.edu/show/qn59q239w65.

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

MLA Handbook (7th Edition):

Harvey, John. “Around Palais' Covering Homotopy Theorem</h1>.” 2014. Web. 01 Dec 2020.

Vancouver:

Harvey J. Around Palais' Covering Homotopy Theorem</h1>. [Internet] [Thesis]. University of Notre Dame; 2014. [cited 2020 Dec 01]. Available from: https://curate.nd.edu/show/qn59q239w65.

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

Council of Science Editors:

Harvey J. Around Palais' Covering Homotopy Theorem</h1>. [Thesis]. University of Notre Dame; 2014. Available from: https://curate.nd.edu/show/qn59q239w65

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


University of Notre Dame

3. Renato G. Bettiol. On different notions of positivity of curvature</h1>.

Degree: Mathematics, 2015, University of Notre Dame

We study interactions between the geometry and topology of Riemannian manifolds that satisfy curvature positivity conditions closely related to positive sectional curvature (sec>0). First, we discuss two notions of weakly positive curvature, defined in terms of averages of pairs of sectional curvatures. The manifold S2 x S2 is proved to satisfy these curvature positivity conditions, implying it satisfies a property intermediate between sec>0 and positive Ricci curvature, and between sec>0 and nonnegative sectional curvature. Combined with surgery techniques, this construction allows to classify (up to homeomorphism) the closed simply-connected 4-manifolds that admit a Riemannian metric for which averages of pairs of sectional curvatures of orthogonal planes are positive. Second, we study the notion of strongly positive curvature, which is intermediate between sec>0 and positive-definiteness of the curvature operator. We elaborate on joint work with Mendes, which yields the classification of simply-connected homogeneous spaces that admit an invariant metric with strongly positive curvature. These methods are then used to study the moduli space of homogeneous metrics with strongly positive curvature on the Wallach flag manifolds and on Berger spheres. Advisors/Committee Members: Gabor Szekelyhidi, Committee Member, Gerard K. Misiolek, Committee Member, Karsten Grove, Committee Chair, Frederico J. Xavier, Committee Member.

Subjects/Keywords: Curvature; 4-manifolds; Riemannian geometry; Sectional curvature; Homogeneous spaces; Curvature operator; Metric deformations

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

APA (6th Edition):

Bettiol, R. G. (2015). On different notions of positivity of curvature</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/rn300z72p6p

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):

Bettiol, Renato G.. “On different notions of positivity of curvature</h1>.” 2015. Thesis, University of Notre Dame. Accessed December 01, 2020. https://curate.nd.edu/show/rn300z72p6p.

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

MLA Handbook (7th Edition):

Bettiol, Renato G.. “On different notions of positivity of curvature</h1>.” 2015. Web. 01 Dec 2020.

Vancouver:

Bettiol RG. On different notions of positivity of curvature</h1>. [Internet] [Thesis]. University of Notre Dame; 2015. [cited 2020 Dec 01]. Available from: https://curate.nd.edu/show/rn300z72p6p.

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

Council of Science Editors:

Bettiol RG. On different notions of positivity of curvature</h1>. [Thesis]. University of Notre Dame; 2015. Available from: https://curate.nd.edu/show/rn300z72p6p

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

.