Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1894303 | Journal of Geometry and Physics | 2009 | 15 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Alexey V. Bolsinov, Vladimir S. Matveev, Giuseppe Pucacco,