Open Access Theses and Dissertations

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You searched for subject:(Isotropic Curvature). Showing records 1 – 3 of 3 total matches.

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Indian Institute of Science

1. Gururaja, H A. Ricci Flow And Isotropic Curvature.

Degree: 2011, Indian Institute of Science

URL: http://hdl.handle.net/2005/2376 

This thesis consists of two parts. In the first part, we study certain Ricci flow invariant nonnegative curvature conditions as given by B. Wilking. We begin by proving that any such nonnegative curvature implies nonnegative isotropic curvature in the Riemannian case and nonnegative orthogonal bisectional curvature in the K¨ahler case. For any closed AdSO(n,C) invariant subset S so(n, C) we consider the notion of positive curvature on S, which we call positive S- curvature. We show that the class of all such subsets can be naturally divided into two subclasses: The first subclass consists of those sets S for which the following holds: If two Riemannian manifolds have positive S- curvature then their connected sum also admits a Riemannian metric of positive S- curvature. The other subclass consists of those sets for which the normalized Ricci flow on a closed Riemannian manifold with positive S-curvature converges to a metric of constant positive sectional curvature. In the second part of the thesis, we study the behavior of Ricci flow for a manifold having positive S - curvature, where S is in the first subclass. More specifically, we study the Ricci flow for a special class of metrics on Sp+1 x S1 , p ≥ 4, which have positive isotropic curvature. Advisors/Committee Members: Seshadri, Harish.

Subjects/Keywords: Ricci Flow; Riemannian Manifolds; Manifolds (Mathematics); Curvature; Isotropic Curvature; S−curvature; Geometry

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

APA (6th Edition):

Gururaja, H. A. (2011). Ricci Flow And Isotropic Curvature. (Thesis). Indian Institute of Science. Retrieved from http://hdl.handle.net/2005/2376

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):

Gururaja, H A. “Ricci Flow And Isotropic Curvature.” 2011. Thesis, Indian Institute of Science. Accessed December 14, 2019. http://hdl.handle.net/2005/2376.

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

MLA Handbook (7th Edition):

Gururaja, H A. “Ricci Flow And Isotropic Curvature.” 2011. Web. 14 Dec 2019.

Vancouver:

Gururaja HA. Ricci Flow And Isotropic Curvature. [Internet] [Thesis]. Indian Institute of Science; 2011. [cited 2019 Dec 14]. Available from: http://hdl.handle.net/2005/2376.

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

Council of Science Editors:

Gururaja HA. Ricci Flow And Isotropic Curvature. [Thesis]. Indian Institute of Science; 2011. Available from: http://hdl.handle.net/2005/2376

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


Indian Institute of Science

2. Gururaja, H A. Ricci Flow And Isotropic Curvature.

Degree: 2011, Indian Institute of Science

URL: http://etd.iisc.ernet.in/handle/2005/2376  ; http://etd.ncsi.iisc.ernet.in/abstracts/3059/G25112-Abs.pdf 

This thesis consists of two parts. In the first part, we study certain Ricci flow invariant nonnegative curvature conditions as given by B. Wilking. We begin by proving that any such nonnegative curvature implies nonnegative isotropic curvature in the Riemannian case and nonnegative orthogonal bisectional curvature in the K¨ahler case. For any closed AdSO(n,C) invariant subset S so(n, C) we consider the notion of positive curvature on S, which we call positive S- curvature. We show that the class of all such subsets can be naturally divided into two subclasses: The first subclass consists of those sets S for which the following holds: If two Riemannian manifolds have positive S- curvature then their connected sum also admits a Riemannian metric of positive S- curvature. The other subclass consists of those sets for which the normalized Ricci flow on a closed Riemannian manifold with positive S-curvature converges to a metric of constant positive sectional curvature. In the second part of the thesis, we study the behavior of Ricci flow for a manifold having positive S - curvature, where S is in the first subclass. More specifically, we study the Ricci flow for a special class of metrics on Sp+1 x S1 , p ≥ 4, which have positive isotropic curvature. Advisors/Committee Members: Seshadri, Harish.

Subjects/Keywords: Ricci Flow; Riemannian Manifolds; Manifolds (Mathematics); Curvature; Isotropic Curvature; S−curvature; Geometry

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❌

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

APA (6th Edition):

Gururaja, H. A. (2011). Ricci Flow And Isotropic Curvature. (Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ernet.in/handle/2005/2376 ; http://etd.ncsi.iisc.ernet.in/abstracts/3059/G25112-Abs.pdf

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):

Gururaja, H A. “Ricci Flow And Isotropic Curvature.” 2011. Thesis, Indian Institute of Science. Accessed December 14, 2019. http://etd.iisc.ernet.in/handle/2005/2376 ; http://etd.ncsi.iisc.ernet.in/abstracts/3059/G25112-Abs.pdf.

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

MLA Handbook (7th Edition):

Gururaja, H A. “Ricci Flow And Isotropic Curvature.” 2011. Web. 14 Dec 2019.

Vancouver:

Gururaja HA. Ricci Flow And Isotropic Curvature. [Internet] [Thesis]. Indian Institute of Science; 2011. [cited 2019 Dec 14]. Available from: http://etd.iisc.ernet.in/handle/2005/2376 ; http://etd.ncsi.iisc.ernet.in/abstracts/3059/G25112-Abs.pdf.

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

Council of Science Editors:

Gururaja HA. Ricci Flow And Isotropic Curvature. [Thesis]. Indian Institute of Science; 2011. Available from: http://etd.iisc.ernet.in/handle/2005/2376 ; http://etd.ncsi.iisc.ernet.in/abstracts/3059/G25112-Abs.pdf

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

3. Moruz, Marilena. Étude des sous-variétés dans les variétés kählériennes, presque kählériennes et les variétés produit : Study of submanifolds of Kaehler manifolds, nearly Kaehler manifolds and product manifolds.

Degree: Docteur es, Mathématiques. Mathématiques pures, 2017, Valenciennes

URL: http://www.theses.fr/2017VALE0003 

Cette thèse est constituée de quatre chapitres. Le premier contient les notions de base qui permettent d'aborder les divers thèmes qui y sont étudiés. Le second est consacré à l'étude des sous-variétés lagrangiennes d'une variété presque kählérienne. J'y présente les résultats obtenus en collaboration avec Burcu Bektas, Joeri Van der Veken et Luc Vrancken. Dans le troisième, je m'intéresse à un problème de géométrie différentielle affine et je donne une classification des hypersphères affines qui sont isotropiques. Ce résultat a été obtenu en collaboration avec Luc Vrancken. Et enfin dans le dernier chapitre, je présente quelques résultats sur les surfaces de translation et les surfaces homothétiques, objet d'un travail en commun avec Rafael López.

Abstract in English not available

Advisors/Committee Members: Vrancken, Luc (thesis director).

Subjects/Keywords: Sous-Variétés lagrangiennes; Lagrangian submanifold; Lagrangian immersion; Riemannian submersion; Affine differential geometry; Blaschke hypersurface; Affine homogeneous; Isotropic difference tensor; Translation surface; Homothetical surface; Mean curvature; Gauss curvature.

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

APA (6th Edition):

Moruz, M. (2017). Étude des sous-variétés dans les variétés kählériennes, presque kählériennes et les variétés produit : Study of submanifolds of Kaehler manifolds, nearly Kaehler manifolds and product manifolds. (Doctoral Dissertation). Valenciennes. Retrieved from http://www.theses.fr/2017VALE0003

Chicago Manual of Style (16th Edition):

Moruz, Marilena. “Étude des sous-variétés dans les variétés kählériennes, presque kählériennes et les variétés produit : Study of submanifolds of Kaehler manifolds, nearly Kaehler manifolds and product manifolds.” 2017. Doctoral Dissertation, Valenciennes. Accessed December 14, 2019. http://www.theses.fr/2017VALE0003.

MLA Handbook (7th Edition):

Moruz, Marilena. “Étude des sous-variétés dans les variétés kählériennes, presque kählériennes et les variétés produit : Study of submanifolds of Kaehler manifolds, nearly Kaehler manifolds and product manifolds.” 2017. Web. 14 Dec 2019.

Vancouver:

Moruz M. Étude des sous-variétés dans les variétés kählériennes, presque kählériennes et les variétés produit : Study of submanifolds of Kaehler manifolds, nearly Kaehler manifolds and product manifolds. [Internet] [Doctoral dissertation]. Valenciennes; 2017. [cited 2019 Dec 14]. Available from: http://www.theses.fr/2017VALE0003.

Council of Science Editors:

Moruz M. Étude des sous-variétés dans les variétés kählériennes, presque kählériennes et les variétés produit : Study of submanifolds of Kaehler manifolds, nearly Kaehler manifolds and product manifolds. [Doctoral Dissertation]. Valenciennes; 2017. Available from: http://www.theses.fr/2017VALE0003

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