[Une version hamiltonienne d’un résultat de Gromoll et Grove]
On généralise aux structures hamiltoniennes réelles sur le théorème qui dit que, dans une -sphère riemannienne dont les géodésiques sont toutes fermées, toute géodésique est simplement fermée. Cela implique que, dans une -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 . For reversible Finsler -spheres all of whose geodesics are closed this implies that the lengths of all geodesics coincide.
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Keywords: Zoll contact forms, Hamiltonian structures, rigidity
Mot 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/}
}
TY - JOUR AU - Frauenfelder, Urs AU - Lange, Christian AU - Suhr, Stefan TI - A Hamiltonian version of a result of Gromoll and Grove JO - Annales de l'Institut Fourier PY - 2019 SP - 409 EP - 419 VL - 69 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.3247/ DO - 10.5802/aif.3247 LA - en ID - AIF_2019__69_1_409_0 ER -
%0 Journal Article %A Frauenfelder, Urs %A Lange, Christian %A Suhr, Stefan %T A Hamiltonian version of a result of Gromoll and Grove %J Annales de l'Institut Fourier %D 2019 %P 409-419 %V 69 %N 1 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.3247/ %R 10.5802/aif.3247 %G en %F 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, 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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