Two-dimensional superintegrable metrics with one linear and one cubic integral
Mathematical Physics
2013-01-14 v1 Analysis of PDEs
Differential Geometry
Dynamical Systems
math.MP
Exactly Solvable and Integrable Systems
Abstract
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
Cite
@article{arxiv.1010.4699,
title = {Two-dimensional superintegrable metrics with one linear and one cubic integral},
author = {Vladimir S. Matveev and Vsevolod V. Shevchishin},
journal= {arXiv preprint arXiv:1010.4699},
year = {2013}
}
Comments
35 pages