Critical point theory of symmetric functions and closed geodesics
type: Item
instance of: scholarly article
title: Critical point theory of symmetric functions and closed geodesics
zbMATH Open document ID: 0874.53035
DOI: 10.1016/S0926-2245(96)00032-0
author: Mónica Clapp
author: Dieter Puppe
published in: Differential Geometry and its Applications
publication date: 1997-10-13T00:00:00Z
review text: The authors consider compact Riemannian manifolds which allow a map \(F\) of a sphere or a projective space into the manifold, which is injective on the homology level. Denote by \(l_{max}\) the maximal length of the image of a circle under \(F\) and by \(l_{min}\) the length of the shortest closed geodesic. In terms of the integer part \(p\) of the quotient \(l_{max}/l_{min}\) the authors obtain lower bounds for the number of geometrically distinct closed geodesics of length \(\leq l_{max}\) (which are called short closed geodesics). For certain values of \(p\) and certain topological types this gives an improvement of known results.
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 58E10
Mathematics Subject Classification ID: 58E40
Mathematics Subject Classification ID: 55P35
Mathematics Subject Classification ID: 55M30
zbMATH DE Number: 1019166
zbMATH Keywords: equivariant critical point theory
zbMATH Keywords: closed geodesics
zbMATH Keywords: free loop space
Wikidata QID: Q115337642
reviewed by: Hans-Bert Rademacher
MaRDI profile type: Publication
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full work available at URL: s0926-2245(96)00032-0
OpenAlex ID: W2059786199
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description: scientific article; zbMATH DE number 1019166