On the multiplicity of isometry-invariant geodesics on product manifolds

Abstract

We prove that on any closed Riemannian manifold $(M_1\times M_2,g)$, with $\rank\Hom_1(M_1)\neq0$ and $\dim (M_2)\ge 2$, every isometry homotopic to the identity admits infinitely many isometry-invariant geodesics.

17 pages

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