Isometry-invariant geodesics and the fundamental group, II

Leonardo Macarini (1) , Marco Mazzucchelli (2)

1 UFRJ - Universidade Federal do Rio de Janeiro [Brasil] = Federal University of Rio de Janeiro [Brazil] = Université fédérale de Rio de Janeiro [Brésil]
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We show that on a closed Riemannian manifold with fundamental group isomorphic to Z, other than the circle, every isometry that is homotopic to the identity possesses infinitely many invariant geodesics. This completes a recent result in [Maz15] of the second author.

Domaines: Mathématiques [math]

Leonardo Macarini, Marco Mazzucchelli. Isometry-invariant geodesics and the fundamental group, II. Advances in Mathematics, 2017, 308, pp.671 - 698. ⟨10.1016/j.aim.2016.12.023⟩. ⟨ensl-01475317⟩