For more information about this meeting, contact Augustin Banyaga, Mari Royer, Aissa Wade, Diane Henderson.
| Title: | Pseudo-Riemannian geodesics and billiards |
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| Seminar: | Symplectic Topology Seminar |
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| Speaker: | Sergei Tabachnikov, PSU |
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| Abstract: |
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| 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 |
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| Date: | 03 / 05 / 2009 |
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| Time: | 01:25pm - 02:15pm |
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