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, Tome 69 (2019) no. 1, pp. 409-419.

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.

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DOI : https://doi.org/10.5802/aif.3247
Classification : 53D35,  53D25
Mots clés : Structures de contact de Zoll, structure hamiltonienne, rigidité
@article{AIF_2019__69_1_409_0,
     author = {Frauenfelder, Urs and Lange, Christian and Suhr, Stefan},
     title = {A Hamiltonian version of a result of Gromoll and Grove},
     journal = {Annales de l'Institut Fourier},
     pages = {409--419},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {69},
     number = {1},
     year = {2019},
     doi = {10.5802/aif.3247},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.3247/}
}
Frauenfelder, Urs; Lange, Christian; Suhr, Stefan. A Hamiltonian version of a result of Gromoll and Grove. Annales de l'Institut Fourier, Tome 69 (2019) no. 1, pp. 409-419. doi : 10.5802/aif.3247. http://archive.numdam.org/articles/10.5802/aif.3247/

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