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

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

1997-12-23

arxiv.org/abs/solv-int/9712019v1

Regular and Chaotic Dynamics, vol 2 no 1 (1997), 96-103

Mathematics

Differential Geometry

10 pages, latex2e

Scientific paper

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.

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