Curvatures of tangent bundles with Cheeger-Gromoll metric
type: Item
instance of: scholarly article
title: Curvatures of tangent bundles with Cheeger-Gromoll metric
zbMATH Open document ID: 0768.53020
author: Masami Sekizawa
published in: Tokyo Journal of Mathematics
publication date: 1992-09-27T00:00:00Z
review text: The author studies the Levi-Civita connection, the Riemannian curvature and the scalar curvature of the Cheeger-Gromoll metric defined on the tangent bundle \(TM\) of an \(n\)-dimensional Riemannian manifold \(M\) [see, for the definition, \textit{J. Cheeger} and \textit{D. Gromoll}, Ann. Math., II. Ser. 96, 413-443 (1972; Zbl 0246.53049)]. The main result of the paper states that the scalar curvature of \(TM\) is non negative if the original metric of \(M\) has constant curvature \(c \geq -3(n-2)/n\), \(n = \dim M\). In particular, this implies that the scalar curvature at \((x,u) \in TM\) is never constant if the orignal metric on \(M\) has constant curvature.
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 60849
zbMATH Keywords: scalar curvature
zbMATH Keywords: constant curvature
reviewed by: Alberto Cavicchioli
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270130381
OpenAlex ID: W2068456002
DOI: 10.3836/TJM/1270130381
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description: scientific article; zbMATH DE number 60849