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. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

Bolsinov, A., Matveev, V., Pucacco, G. (2009). Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta. JOURNAL OF GEOMETRY AND PHYSICS, 59(7), 1048-1062 [10.1016/j.geomphys.2009.04.010].

Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta

PUCACCO, GIUSEPPE
2009-01-01

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. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.
2009
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/07 - FISICA MATEMATICA
English
Geodesically equivalent metrics; Integrable systems; Separability by quadrature
Bolsinov, A., Matveev, V., Pucacco, G. (2009). Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta. JOURNAL OF GEOMETRY AND PHYSICS, 59(7), 1048-1062 [10.1016/j.geomphys.2009.04.010].
Bolsinov, A; Matveev, V; Pucacco, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/33171
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