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On riemannian manifolds whose tangent sphere bundles can have nonnegative sectional curvature
Oldřich Kowalski,Masami Sekizawa +1 more
- pp 245-256
TLDR
In this article, the sectional curvature of tangent sphere bundles over locally symmetric Riemannian manifolds has been studied, and it has been shown that the converse of Theorem 1 also holds.Abstract:
The authors proved a theorem about the sectional curvature of tangent sphere bundles over locally symmetric Riemannian manifolds (see Theorem A below). After a slight generalization of this theorem (Theo- rem 1) we prove several results which give strong support of the conjecture that the converse of Theorem 1 also holds. The problem still remains open, in general.read more
Citations
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On Riemannian geometry of tangent sphere bundles with arbitrary constant radius
Oldřich Kowalski,Masami Sekizawa +1 more
TL;DR: In this article, a survey of Riemannian geometry of tangent sphere bundles with arbitrary constant radius can be found, with a focus on tangent spheres with constant radius.
Characterization of the Unit Tangent Sphere Bundle with $ g $-Natural Metric and Almost Contact B-metric Structure
TL;DR: In this paper, the authors considered unit tangent sphere bundle of a Riemannian manifold M,g as a 2n+1-dimensional manifold and equipped it with pseudo-Riemannians with a natural almost contact B-metric structure.
References
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Journal Article
Characteristic reflections on unit tangent sphere bundles
Eric Boeckx,Lieven Vanhecke +1 more
Journal ArticleDOI
Unit Tangent Sphere Bundles with Constant Scalar Curvature
Eric Boeckx,Lieven Vanhecke +1 more
TL;DR: In this article, the authors derived necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature and gave complete classifications for low dimensions and for conformally flat manifolds.
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On Tangent Sphere Bundles with Small or Large Constant Radius
Oldřich Kowalski,Masami Sekizawa +1 more
TL;DR: For a Riemannian manifold M, the induced Sasaki metric of a tangent sphere bundle is defined in this article for the case when the constant radius r > 0 of the tangent spheres is either sufficiently small or sufficiently large.
Journal ArticleDOI
Conformally flat Riemannian manifolds admitting a transitive group of isometries, II
TL;DR: In this article, the authors classify conformally flat Riemannian manifolds admitting a transitive group of isometries and give the classification together with Theorem D in Section 4.
Journal ArticleDOI
The sectional curvature of the Sasaki metric of T1Mn
TL;DR: In this paper, the authors studied the sectional curvature of the Sasaki metric on the tangent bundle of vectors of fixed length on a Riemannian manifold and gave sufficient conditions for the curvature to be nonnegative.