Two-dimensional superintegrable metrics with one linear and one cubic integral

Details Two-dimensional superintegrable metrics with one linear and one cubic integral Two-dimensional superintegrable metrics with one linear and one cubic integral

2010-10-22

arxiv.org/abs/1010.4699v1

Journal of Geometry and Physics 61(2011) , no. 8, 1353-1377

Physics

Mathematical Physics

35 pages

Scientific paper

We describe all local Riemannian metrics on surfaces whose geodesic flows are superintegrable with one integral linear in momenta and one integral cubic in momenta. We also show that some of these metrics can be extended to the 2-sphere. This gives us new examples of Hamiltonian systems on the sphere with integrals of degree three in momenta, and the first examples of superintegrable metrics of nonconstant curvature on a closed surface

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