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

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.

arXiv comment10 pages, latex2e

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