A Hamiltonian version of a result of Gromoll and Grove  [ Une version hamiltonienne d’un résultat de Gromoll et Grove ]
Annales de l'Institut Fourier, à paraître, 11 p.

On généralise aux structures hamiltoniennes réelles sur P 3 le théorème qui dit que, dans une 2-sphère riemannienne dont les géodésiques sont toutes fermées, toute géodésique est simplement fermée. Cela implique que, dans une 2-sphère finslerienne réversible dont les géodésiques sont toutes fermées, elles ont toutes la même longueur.

The theorem that if all geodesics of a Riemannian two-sphere are closed they are also simple closed is generalized to real Hamiltonian structures on P 3 . For reversible Finsler 2-spheres all of whose geodesics are closed this implies that the lengths of all geodesics coincide.

Reçu le : 2016-04-06
Révisé le : 2018-02-27
Accepté le : 2018-03-13
Publié le : 2019-03-08
Classification:  53D35,  53D25
Mots clés: Structures de contact de Zoll, structure hamiltonienne, rigidité
@unpublished{AIF_0__0_0_A11_0,
     author = {Frauenfelder, Urs and Lange, Christian and Suhr, Stefan},
     title = {A Hamiltonian version of a result of Gromoll and Grove},
     note = {to appear in \emph{Annales de l'Institut Fourier}},
}
Frauenfelder, Urs; Lange, Christian; Suhr, Stefan. A Hamiltonian version of a result of Gromoll and Grove. Annales de l'Institut Fourier, à paraître, 11 p.

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