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