Isometry-invariant geodesics and the fundamental group, II

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 [20] of the second author.

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2017-02, Vol.308, p.671-698, Article 671
Main Authors: Macarini, Leonardo, Mazzucchelli, Marco
Format: Article
Language:English
Subjects:
Closed geodesics
Isometry-invariant geodesics
Mathematics
Morse theory
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Description
Summary: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 [20] of the second author.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2016.12.023