On the multiplicity of isometry-invariant geodesics on product manifolds

Mazzucchelli, Marco¹

¹Unité de Mathématiques Pures et Appliquées, École Normale Supérieure de Lyon, 46 allée d’Italie, 69364 Lyon Cedex 07, France

Algebraic and Geometric Topology, Tome 14 (2014) no. 1, pp. 135-156

Résumé

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.

Détail

DOI : 10.2140/agt.2014.14.135

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

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