Article ID Journal Published Year Pages File Type
1894303 Journal of Geometry and Physics 2009 15 Pages PDF
Abstract

We discuss pseudo-Riemannian metrics on 2-dimensional manifolds such that the geodesic flow admits a nontrivial integral quadratic in velocities. We construct local normal forms of such metrics. We show that these metrics have certain useful properties similar to those of Riemannian Liouville metrics, namely: •they admit geodesically equivalent metrics;•one can use them to construct a large family of natural systems admitting integrals quadratic in momenta;•the integrability of such systems can be generalized to the quantum setting;•these natural systems are integrable by quadratures.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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