On the multiplicity of isometry-invariant geodesics on product manifolds
classification
🧮 math.DG
keywords
geodesicsisometry-invariantadmitsclosedeverygeq2homotopicidentity
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We prove that on any closed Riemannian manifold $(M_1\times M_2,g)$, with $\rank\Hom_1(M_1)\neq0$ and $\dim(M_2)\geq2$, every isometry homotopic to the identity admits infinitely many isometry-invariant geodesics.
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