On the existence of infinitely many closed geodesics on non-compact manifolds

Luca Asselle; Marco Mazzucchelli

On the existence of infinitely many closed geodesics on non-compact manifolds

Luca Asselle ¹ Marco Mazzucchelli ²

1 Ruhr-Universitat Bochum, Fakultat fur Mathematik

2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

Abstract : We prove that any complete (and possibly non-compact) Rie-mannian manifold M possesses infinitely many closed geodesics provided its free loop space has unbounded Betti numbers in degrees larger than dim(M), and there are no close conjugate points at infinity. Our argument builds on an existence result due to Benci and Giannoni, and generalizes the celebrated theorem of Gromoll and Meyer for closed manifolds.

Document type :

Journal articles

Domain :

Mathematics [math] / Differential Geometry [math.DG]

Mathematics [math] / Dynamical Systems [math.DS]

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https://hal-ens-lyon.archives-ouvertes.fr/ensl-01520339
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Submitted on : Wednesday, May 10, 2017 - 1:25:38 PM
Last modification on : Thursday, January 11, 2018 - 6:12:31 AM
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On the existence of infinitely many closed geodesics on non-compact manifolds

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