PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Augustin Banyaga, Mari Royer, Aissa Wade, Diane Henderson.

Title:Pseudo-Riemannian geodesics and billiards
Seminar:Symplectic Topology Seminar
Speaker:Sergei Tabachnikov, PSU
Abstract:
Many classical facts in Riemannian geometry have pseudo-Riemannian analogs. For instance, 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. I shall discuss the geometry of these structures in some detail, and introduce and study pseudo-Euclidean billiards that have some peculiar properties. Pseudo-Euclidean analogs of the Jacobi-Chasles theorems and the integrability of the billiard inside an ellipsoid in pseudo-Euclidean space will be discussed, as well as a Poncelet- style closure theorem for null geodesics on an ellipsoid in Minkowski space. Based on a joint work with B. Khesin.

Room Reservation Information

Room Number:MB315
Date:03 / 05 / 2009
Time:01:25pm - 02:15pm