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

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 and prove the nonexistence of quadratically-superintegrable metrics of nonconstant curvature on closed surfaces

This paper has been withdrawn by the author. This paper is now, together with the paper arXiv:1002.0133, a part of the paper arXiv:1002.3934

References in corpus (4)

• A solution of a problem of Sophus Lie: Normal forms of 2-dim metrics admitting two projective vector fields
• Invariant characterization of Liouville metrics and polynomial integrals
• Geometrical classification of Killing tensors on bidimensional flat manifolds
• Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta