On the multiplicity of isometry-invariant geodesics on product manifolds

Mazzucchelli, Marco

doi:10.2140/agt.2014.14.135

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On the multiplicity of isometry-invariant geodesics on product manifolds

Marco Mazzucchelli

Algebraic & Geometric Topology 14 (2014) 135–156

DOI: 10.2140/agt.2014.14.135

Abstract

We prove that on any closed Riemannian manifold $(M_{1} \times M_{2}, g)$ , with $dim (M_{2}) \geq 2$ and $rank H_{1} (M_{1}) \neq 0$ , 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/

Volume 14, issue 1 (2014)