Explicit metrics for a class of two-dimensional superintegrable systems

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

References in corpus (3)

• Two-dimensional superintegrable metrics with one linear and one cubic integral
• On a class of integrable systems with a quartic first integral
• Zoll and Tannery metrics from a superintegrable geodesic flow

Cited by in corpus (8)

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• Integrable Cosmological Potentials
• Global structure and geodesics for Koenigs superintegrable systems
• (Super-)integrable systems associated to 2-dimensional projective connections with one projective symmetry
• Koenigs Theorem and Superintegrable Liouville Metrics
• Real-analyticity of 2-dimensional superintegrable metrics and solution of two Bolsinov-Kozlov-Fomenko conjectures
• Hexagonal geodesic 3-webs
• Superintegrable metrics on surfaces admitting integrals of degrees 1 and 4