English

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

Differential Geometry 2010-10-25 v2 Mathematical Physics math.MP

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

Keywords

Cite

@article{arxiv.0911.3521,
  title  = {Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta},
  author = {Vladimir S. Matveev},
  journal= {arXiv preprint arXiv:0911.3521},
  year   = {2010}
}

Comments

This paper has been withdrawn by the author.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