Explicit metrics for a class of two-dimensional superintegrable systems
arXiv:1403.0422 · doi:10.1016/j.geomphys.2014.08.004
Abstract
We obtain, in local coordinates, the explicit form of the two-dimensional, super-integrable systems of Matveev and Shevchishin involving cubic integrals. This enables us to determine for which values of the parameters these systems are indeed globally defined on the two-sphere.
10 pages, no figure, to appear in the Proceedings of the Conference: "Finite dimensional integrable systems", 15th-19th of July 2013, CIRM, Luminy Campus, Marseille (France) published in the Journal of Geometry and Physics