Isometry-invariant geodesics and the fundamental group, II

Abstract

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

23 pages. Version 2: added the proof of Lemma 2.2. To appear in Advances in Mathematics

References in corpus (1)

• Isometry-invariant geodesics and the fundamental group

Cited by in corpus (1)

• On Tonelli periodic orbits with low energy on surfaces