Complete open manifolds of non-negative radial curvature
type: Item
instance of: scholarly article
title: Complete open manifolds of non-negative radial curvature
zbMATH Open document ID: 0818.53055
author: Yoshiroh Machigashira
published in: Pacific Journal of Mathematics
publication date: 1995-08-01T00:00:00Z
review text: Let \(M\) be a complete, connected Riemannian manifold and let \(x\in M\). Suppose that \(\delta\) is a lower bound for the sectional curvature of those planes \(\sigma\) in \(M\) that are tangent to a minimal geodesic from \(x\) to the foot point of \(\sigma\). Then triangle comparison holds for geodesic triangles with a vertex in \(x\). The author concludes, among other things, that the set of critical points of the distance function to \(x\) is bounded if \(\delta=0\).
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 695069
zbMATH Keywords: radial sectional curvature
zbMATH Keywords: triangle comparison
reviewed by: Werner Ballmann
MaRDI profile type: Publication
full work available at URL: pjm.1994.165.153
OpenAlex ID: W2095275985
Wikidata QID: Q126095909
DOI: 10.2140/PJM.1994.165.153
description: scientific article; zbMATH DE number 695069