Cohomogeneity and positive curvature in low dimensions
type: Item
instance of: scholarly article
title: Cohomogeneity and positive curvature in low dimensions
zbMATH Open document ID: 0804.53057
DOI: 10.1007/BF02572419
author: Catherine Searle
published in: Mathematische Zeitschrift
publication date: 1994-05-10T00:00:00Z
full work available at URL: https://eudml.org/doc/174583
review text: The classification of compact positively curved Riemannian manifolds (CPCM's) is a basic problem. A compact, connected Lie group \(G\) is said to act by cohomogeneity \(k\) on a Riemannian manifold if \(G\) acts effectively and isometrically with a principal orbit of codimension \(k\). The main result of the paper is the following: if \(M^ n\), \(2\leq n\leq 6\), is a simply connected CPCM admitting a cohomogeneity one action with respect to this metric, then \(M^ n\) is diffeomorphic to either \(S^ n\) or \(CP^{n/2}\).
reviewed by: A. P. Stone
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C10
zbMATH DE Number: 567456
zbMATH Keywords: Riemannian manifolds
zbMATH Keywords: principal orbit
zbMATH Keywords: cohomogeneity one action
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 567456