Stefan Suhr (Ruhr-Universität Bochum) : A Hamiltonian version of a result of Gromoll and Grove

mercredi 28 mars 2018, 14:00 → 15:00 Europe/Paris

Many problem on closed geodesics in Riemannian manifolds have a reformulation as a symplectic or contact geometric problem. A celebrated result in the theory of Riemannian metrics all of whose geodesics are closed is the theorem of Gromoll and Grove asserting that the geodesics of a Riemannian metric on the 2-sphere all of whose geodesics are closed are simple closed. This implies especially that all geodesics have a common minimal period. I will explain how generalize this theorem to real Hamiltonian structures, which includes contact structures, on the 3-dimensional real projective space. As a corollary one obtains that for reversible Finsler metrics all geodesics have the same length if they are all closed.