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This paper has been withdrawn by the author.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