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

Luca Asselle; Marco Mazzucchelli

doi:10.1090/proc/13398

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.

Type de document :

Article dans une revue

Proceedings of the American Mathematical Society, American Mathematical Society, 2016, 145, pp.2689 - 2697. 〈10.1090/proc/13398〉

Domaine :

Mathématiques [math] / Géométrie différentielle [math.DG]

Mathématiques [math] / Systèmes dynamiques [math.DS]

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https://hal-ens-lyon.archives-ouvertes.fr/ensl-01520339
Contributeur : Marco Mazzucchelli <>
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