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On the multiplicity of isometry-invariant geodesics on product manifolds

Marco Mazzucchelli

Algebraic & Geometric Topology 14 (2014) 135–156
Abstract

We prove that on any closed Riemannian manifold (M1 × M2,g), with dim(M2) 2 and rankH1(M1)0, every isometry homotopic to the identity admits infinitely many isometry-invariant geodesics.

Keywords
isometry-invariant geodesics, closed geodesics, Morse theory
Mathematical Subject Classification 2010
Primary: 58E10
Secondary: 53C22
References
Publication
Received: 14 May 2012
Revised: 28 July 2013
Accepted: 31 July 2013
Preview posted: 21 November 2013
Published: 9 January 2014
Authors
Marco Mazzucchelli
Unité de Mathématiques Pures et Appliquées
École Normale Supérieure de Lyon
46 allée d’Italie
69364 Lyon Cedex 07
France
http://perso.ens-lyon.fr/marco.mazzucchelli/