Volume 14, issue 1 (2014)

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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 $\left({M}_{1}×{M}_{2},g\right)$, with $dim\left({M}_{2}\right)\ge 2$ and $rank\phantom{\rule{0.3em}{0ex}}{H}_{1}\left({M}_{1}\right)\ne 0$, every isometry homotopic to the identity admits infinitely many isometry-invariant geodesics.

Keywords
isometry-invariant geodesics, closed geodesics, Morse theory
Primary: 58E10
Secondary: 53C22