Geodesic equivalence and integrability

Details Geodesic equivalence and integrability Geodesic equivalence and integrability

1999-11-10

arxiv.org/abs/math/9911062v1

MPIM preprint series, no. 74 (1998)

Mathematics

Differential Geometry

19 pages; LaTeX

Scientific paper

We suggest a construction that, given a trajectorial diffeomorphism between
two Hamiltonian systems, produces integrals of them.
As the main example we treat geodesic equivalence of metrics.
We show that the existence of a non-trivially geodesically equivalent metric
leads to Liouville integrability, and present explicit formulae for integrals.

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