A Hamiltonian version of a result of Gromoll and Grove
Annales de l'Institut Fourier, Volume 69 (2019) no. 1, pp. 409-419.

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.

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.

Received: 2016-04-06
Revised: 2018-02-27
Accepted: 2018-03-13
Published online: 2019-06-03
DOI: https://doi.org/10.5802/aif.3247
Classification: 53D35,  53D25
Keywords: Zoll contact forms, Hamiltonian structures, rigidity
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {69},
     number = {1},
     year = {2019},
     pages = {409-419},
     doi = {10.5802/aif.3247},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2019__69_1_409_0/}
}
Frauenfelder, Urs; Lange, Christian; Suhr, Stefan. A Hamiltonian version of a result of Gromoll and Grove. Annales de l'Institut Fourier, Volume 69 (2019) no. 1, pp. 409-419. doi : 10.5802/aif.3247. https://aif.centre-mersenne.org/item/AIF_2019__69_1_409_0/

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