A generalization of the Cheeger-Gromoll splitting theorem
type: Item
instance of: scholarly article
title: A generalization of the Cheeger-Gromoll splitting theorem
zbMATH Open document ID: 0614.53032
DOI: 10.1007/BF01191365
author: Gregory J. Galloway
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: The original theorem of \textit{J. Cheeger} and \textit{D. Gromoll} [J. Differ. Geom. 6, 119-128 (1971; Zbl 0223.53033)] states that a complete connected Riemannian manifold M splits isometrically as a product \({\mathbb{R}}\times M'\) if the Ricci curvature of M is nonnegative and M contains a line. In the present paper, the curvature assumption is weakened to an average version, namely that along each ray \(\sigma\) the limes inferior of \(\int^{t}_{0}Ric(\sigma '(s),\sigma '(s))ds\) for \(t\to \infty\) is nonnegative. The essential point is the subharmonicity of Busemann functions under the given curvature condition.
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 3994460
zbMATH Keywords: splitting theorem
zbMATH Keywords: Busemann functions
reviewed by: Rolf Walter
MaRDI profile type: Publication
cites work: A theorem of Myers
cites work: The splitting theorem for manifolds of nonnegative Ricci curvature
cites work: Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds
cites work: An elementary proof of the Cheeger-Gromoll splitting theorem
cites work: Some results on the occurrence of compact minimal submanifolds
cites work: Compactness Criteria for Riemannian Manifolds
cites work: An elementary method in the study of nonnegative curvature
Wikidata QID: Q126014090
description: scientific article; zbMATH DE number 3994460