Invariant characterization of Liouville metrics and polynomial integrals
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.
Dette er forfatternes aksepterte versjon. This is the author’s final accepted manuscript.
CitationJournal of Geometry and Physics 58 (2008) 979–995 doi:10.1016/j.geomphys.2008.03.005
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