闭曲面上测地流允许动量二次非平凡积分的伪黎曼度量
微分几何
2010-10-25 v2 数学物理
math.MP
摘要
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
引用
@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}
}
备注
This paper has been withdrawn by the author.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