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Exterior Differential Systems and the Method of Equivalence |
| May 05, 2008 to May 09, 2008 |
| Organized By: Jeanne Clelland, William F. Shadwick (Chair) and George Wilkens |
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| Return to Workshop Description |
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Integrals quadratic in velocities and solution of two problems of Sophus Lie
Thursday May 8, 2008
11:00AM - 12:00PM
Speakers:
Vladimir Matveev
Abstract:
Integrals quadratic in velocities and solution of two problems of Sophus Lie
Abstract: In 1882 Sophus Lie asked to describe all 2-dimensional metrics admitting vector fields whose flows sends (unparameterized) geodesics to geodesics. I will explain the solution of this problem (part of the results are joint with R.L. Bryant and G. Manno). The results are published in arXiv:0705.3592, arXiv:0802.2344, and arXiv:0802.2346. The solution uses a description of metrics whose geodesic flows admit integrals quadratic in velocities; I will give an overview of this subject.
Besides this theory, the solution consists of a trick and huge calculations. I will explain the trick and hope you will explain me what other classical problems one can hope to solve by using similar calculations.
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