English

Quadratically integrable geodesic flows on the torus and on the Klein bottle

solv-int 2011-08-22 v1 Differential Geometry Exactly Solvable and Integrable Systems

Abstract

In the present paper we prove, that if the geodesic flow of a metric G on the torus T is quadratically integrable, then the torus T isometrically covers a torus with a Liouville metric on it, and describe the set of quadratically integrable geodesic flows on the Klein bottle.

Cite

@article{arxiv.solv-int/9712019,
  title  = {Quadratically integrable geodesic flows on the torus and on the Klein bottle},
  author = {V. S. Matveev},
  journal= {arXiv preprint arXiv:solv-int/9712019},
  year   = {2011}
}

Comments

10 pages, latex2e

R2 v1 2026-07-22T20:08:33.223Z