Quebec Mathematical Sciences Colloquium

October 26, 2007 from 16:00 to 18:00 (Montreal/Miami time) On location

Pseudo-Riemannian geodesics and billiards

Colloquium presented by Boris Khesin (University of Toronto)

In pseudo-Riemannian geometry the spaces of space-like and time-like geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. Furthermore, the space of all geodesics has a structure of a Jacobi manifold. In the talk I will describe the geometry of these structures, define pseudo-Euclidean billiards and discuss their properties. In particular, I will outline complete integrability of the billiard in the ellipsoid and the geodesic flow on the ellipsoid in pseudo-Euclidean space; these results are pseudo-Euclidean counterparts to the classical theorems of Euclidean geometry that go back to Jacobi and Chasles.


UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., room SH-3420