On tangent sphere bundles with small or large constant radius
type: Item
instance of: scholarly article
title: On tangent sphere bundles with small or large constant radius
zbMATH Open document ID: 1011.53025
DOI: 10.1023/A:1006707521207
author: Oldřich Kowalski
author: Masami Sekizawa
published in: Annals of Global Analysis and Geometry
publication date: 2003-06-04T00:00:00Z
review text: For an \(n\)-dimensional Riemannian manifold \(M\), the authors determine some curvature properties of a tangent sphere bundle \(\text{Tr M}\) endowed with the induced Sasaki metric. For instance, let \((M,g)\), \(n>2,\) be a Riemannian manifold with bounded sectional curvature. Then, for each sufficiently small radius \(r\), the tangent sphere bundle is a space of positive scalar curvature. For a compact Riemannian manifold with positive Ricci curvature, the tangent sphere bundle is a space of positive Ricci curvature, in the case when the radius \(r\) is sufficiently small. Let \((M,g),\) \(n>1,\) be a \(d\)-pinched Riemannian manifold. Then, for each sufficiently large radius \(r\), the tangent sphere bundle is a space of negative scalar curvature.
reviewed by: Valentin Boju
Mathematics Subject Classification ID: 53C07
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 1530048
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: Riemannian submersion
zbMATH Keywords: Sasaki metric
zbMATH Keywords: tangent sphere bundle
zbMATH Keywords: variation of a Riemannian metric
MaRDI profile type: Publication
full work available at URL: a:1006707521207
OpenAlex ID: W1560048608
description: scientific article; zbMATH DE number 1530048