Diameter, volume, and topology for positive Ricci curvature
type: Item
instance of: scholarly article
title: Diameter, volume, and topology for positive Ricci curvature
zbMATH Open document ID: 0724.53026
author: J.-H. Eschenburg
published in: Journal of Differential Geometry
publication date: 1991-01-01T00:00:00Z
review text: The author establishes the following result: Let \(M^ n\) be a compact Riemannian manifold with Ricci curvature \(\geq 1\). There is a number \(\epsilon >0\) such that for \(diam(M)>\pi -\epsilon\), \(M^ n\) is homeomorphic to the unit n-sphere. We remark that \(\epsilon\) depends on n, on a lower bound of the sectional curvature of \(M^ n\) and on a lower bound of the injectivity radius. The lemma used to prove the previous result allows to deduce a known theorem: If \(M^ n\) is a compact Riemannian manifold with sectional curvature \(\geq 1\) and \(diam(M)>\pi /2\), then \(M^ n\) is homeomorphic to a sphere.
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 4194624
zbMATH Keywords: diameter
zbMATH Keywords: volume
zbMATH Keywords: Ricci curvature
zbMATH Keywords: sectional curvature
zbMATH Keywords: homeomorphic to a sphere
Wikidata QID: Q115181597
reviewed by: I. D. Albu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214446563
OpenAlex ID: W1550532787
DOI: 10.4310/JDG/1214446563
description: scientific article; zbMATH DE number 4194624