Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta, and proof of the projective Obata conjecture for two-dimensional pseudo-Riemannian metrics

Abstract

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, prove the nonexistence of quadratically-superintegrable metrics of nonconstant curvature on closed surfaces, and prove the two-dimensional pseudo-Riemannian version of the projective Obata conjecture.

33 pages, 7 pictures. This paper replaces arXiv:0911.3521v1 and arXiv:1002.0133

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Cited by in corpus (2)

• Open problems and questions about geodesics
• Open Problems, Questions, and Challenges in Finite-Dimensional Integrable Systems