no. 1
A Hamiltonian version of a result of Gromoll and Grove
[Une version hamiltonienne d’un résultat de Gromoll et Grove]
Frauenfelder, Urs1 ; Lange, Christian2 ; Suhr, Stefan3
1 Institut für Mathematik Universität Augsburg Universitätsstrasse 14 86159 Augsburg (Germany)
2 Mathematisches Institut Universität zu Köln Weyertal 86-90 50931 Cologne (Germany)
3 DMA, ENS Paris and Université Paris Dauphine 45 rue d’Ulm 75005 Paris (France)
Annales de l'Institut Fourier, Tome 69 (2019) no. 1, pp. 409-419.

On généralise aux structures hamiltoniennes réelles sur ℝP 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 ℝP 3 . For reversible Finsler 2-spheres all of whose geodesics are closed this implies that the lengths of all geodesics coincide.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3247
Classification : 53D35, 53D25
Keywords: Zoll contact forms, Hamiltonian structures, rigidity
Mot clés : Structures de contact de Zoll, structure hamiltonienne, rigidité

Frauenfelder, Urs 1 ; Lange, Christian 2 ; Suhr, Stefan 3

1 Institut für Mathematik Universität Augsburg Universitätsstrasse 14 86159 Augsburg (Germany)
2 Mathematisches Institut Universität zu Köln Weyertal 86-90 50931 Cologne (Germany)
3 DMA, ENS Paris and Université Paris Dauphine 45 rue d’Ulm 75005 Paris (France)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.3247/

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