Actions libres et isométriques sur les variétés à géodésiques toutes fermées de même longueur
type: Item
instance of: scholarly article
title: Actions libres et isométriques sur les variétés à géodésiques toutes fermées de même longueur
zbMATH Open document ID: 0549.53041
DOI: 10.1007/BF01773384
author: J. Breuneval
author: F. Pecaut
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1984-01-01T00:00:00Z
review text: It is proved that a Lie group which operates freely and through isometries on a Riemannian manifold M all of whose geodesics are closed is \(S^ 1\), \(S^ 3\) or SO(3). If M is \(S^{2n+1}\) or \(S^{4n+3}\) then it is \(S^ 1\) or \(S^ 3\) respectively.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 3876128
zbMATH Keywords: Lie group
zbMATH Keywords: isometries
zbMATH Keywords: geodesics
reviewed by: Gudlaugur Thorbergsson
MaRDI profile type: Publication
cites work: Relations on Iterated Reduced Powers
cites work: Sur quelques variétés riemanniennes suffisamment pincées
cites work: Q3857363
cites work: Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
cites work: Q5341449
cites work: Q5658847
cites work: Q4169382
cites work: Q5842420
cites work: Riemannian submersions with totally geodesic fibers
cites work: Spaces With a Compact Lie Group of Transformations
cites work: Q5731354
cites work: Characteristic Classes. (AM-76)
cites work: Q5546515
full work available at URL: https://doi.org/10.1007/bf01773384
OpenAlex ID: W2328360113
Recommended article: Q5472629
Recommended article: Free, isometric circle actions on compact symmetric spaces
Recommended article: Q3344797
Recommended article: Isometric actions on pseudo-Riemannian nilmanifolds
Recommended article: Isometry actions and geodesics orthogonal to submanifolds
Recommended article: Q3471225
Recommended article: Q3805407
Recommended article: Geometry of nondegenerate \({\mathbb R}^n\)-actions on \(n\)-manifolds
description: scientific article; zbMATH DE number 3876128