Isometry-invariant geodesics on spheres
type: Item
instance of: scholarly article
title: Isometry-invariant geodesics on spheres
zbMATH Open document ID: 0667.53038
DOI: 10.1215/S0012-7094-88-05733-X
author: Nancy Hingston
published in: Duke Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: For most closed Riemannian manifolds any isometry will have infinitely many invariant geodesics for topological reasons [cf. the reviewer and \textit{S. Halperin}, Publ. Math., Inst. Hautes Etud. Sci. 56, 171-178 (1982; Zbl 0508.55013)]. This is not the case for the simplest manifolds such as e.g. spheres, where indeed for the standard metric almost any isometry will have only finitely many invariant geodesics. In contrast, however, the author proves the interesting result that (finite order) isometries for generic metrics of spheres have infinitely many invariant geodesics.
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 58E10
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
zbMATH DE Number: 4092285
zbMATH Keywords: invariant geodesics
zbMATH Keywords: isometries
zbMATH Keywords: generic metrics
zbMATH Keywords: spheres
reviewed by: Karsten Grove
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4092285