University of Toronto's Symplectic Geometry Seminar

Abstract: The space of geodesics of a Riemannian manifold carries a canonical symplectic structure. In pseudo-Riemannian case, there three types of geodesics: space-, time- and light-like; the former two carry symplectic and the latter a contact structure. I will define pseudo- Euclidean billiards and explain 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.