Global Differential Geometry: Global theory of geodesically equivalent metrics.

I am trying to understand under what conditions a diffeomorphism of a closed manifold preserving (unparameterised) geodesics must be a homothety. During the first phase of the project I understood completely the Riemannian case. My current goal is to study the pseudo-Riemannian case. More precisely, I hope to solve the Beltrami Problem for closed pseudo-Riemannian 2-manifolds, to prove or disprove in the pseudo-Riemannian case the Projective Lichnerowicz-Obata Conjecture, and to find first obstructions preventing a closed manifold from possessing different pseudo-Riemannian metrics sharing the same geodesics.

contact person: PD Dr. Vladimir Matveev
Phone: 0761/203-5578
Email: matveev@email.mathematik.uni-freiburg.de

Start of project: 01.06.2003
End of project: 30.09.2006

Albert-Ludwigs-University Freiburg
PD Dr. Vladimir Matveev

Actual Research Report