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

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〉
Liste complète des métadonnées

Littérature citée [17 références]  Voir  Masquer  Télécharger

https://hal-ens-lyon.archives-ouvertes.fr/ensl-01520339
Contributeur : Marco Mazzucchelli <>
Soumis le : mercredi 10 mai 2017 - 13:25:38
Dernière modification le : jeudi 11 janvier 2018 - 06:12:31
Document(s) archivé(s) le : vendredi 11 août 2017 - 13:00:35

Fichier

non_compact.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Luca Asselle, Marco Mazzucchelli. On the existence of infinitely many closed geodesics on non-compact manifolds. Proceedings of the American Mathematical Society, American Mathematical Society, 2016, 145, pp.2689 - 2697. 〈10.1090/proc/13398〉. 〈ensl-01520339〉

Partager

Métriques

Consultations de la notice

63

Téléchargements de fichiers

32