Invariant characterization of Liouville metrics and polynomial integrals
Differential Geometry
2009-11-13 v1 Mathematical Physics
math.MP
Abstract
A criterion in terms of differential invariants for a metric on a surface to be Liouville is established. Moreover, in this paper we completely solve in invariant terms the local mobility problem of a 2D metric, considered by Darboux: How many quadratic in momenta integrals does the geodesic flow of a given metric possess? The method is also applied to recognition of other polynomial integrals of geodesic flows.
Keywords
Cite
@article{arxiv.0709.0423,
title = {Invariant characterization of Liouville metrics and polynomial integrals},
author = {Boris Kruglikov},
journal= {arXiv preprint arXiv:0709.0423},
year = {2009}
}