Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta

Details Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta

2009-11-18

arxiv.org/abs/0911.3521v2

Mathematics

Differential Geometry

This paper has been withdrawn by the author. This paper is now, together with the paper arXiv:1002.0133, a part of the paper a

Scientific paper

We describe all pseudo-Riemannian metrics on closed surfaces whose geodesic
flows admit nontrivial integrals quadratic in momenta. As an application, we
solve the Beltrami problem on closed surfaces and prove the nonexistence of
quadratically-superintegrable metrics of nonconstant curvature on closed
surfaces

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