Curvature at infinity of open nonnegatively curved manifolds
type: Item
instance of: scholarly article
title: Curvature at infinity of open nonnegatively curved manifolds
zbMATH Open document ID: 0678.53031
author: J.-H. Eschenburg
author: Martin Strake
author: Viktor Schroeder
published in: Journal of Differential Geometry
publication date: 1989-01-01T00:00:00Z
review text: Let \(\Sigma\) be a soul of a complete open Riemannian manifold of nonnegative sectional curvature. Let \(\kappa\) (t) be the maximum of the curvature at all points of M with the distance \(\geq t\) from \(\Sigma\). The authors obtain a bound on the decay of the function \(\kappa\) under suitable topological conditions. Among others, if \(n=\dim M\) is odd, \(k=\dim \Sigma\), \(\alpha =2-2k/(n-1)\) and \(\chi\) (M)\(\neq 0\), then either lim sup \(\kappa\) (t)t\({}^{\alpha}>0\) or M is a flat Euclidean space.
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 4111490
zbMATH Keywords: soul
zbMATH Keywords: nonnegative sectional curvature
zbMATH Keywords: decay
reviewed by: Paweł Walczak
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214443288
OpenAlex ID: W1546793095
Wikidata QID: Q115182625
DOI: 10.4310/JDG/1214443288
description: scientific article; zbMATH DE number 4111490