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

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Matveev, Vladimir S.¹  Shevchishin, Vsevolod V.² 

[1] Univ Jena, Math Inst, D-07737 Jena, Germany

[2] Univ Hamburg, Dept Math, D-20146 Hamburg, Germany

关键词: Polynomially integrable geodesic flows on surfaces;    Solvability of PDE;    Superintegrable systems;    Killing vector fields;   

DOI  :  10.1016/j.geomphys.2011.02.012

来源: Elsevier

【 摘 要 】

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 S(2). 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. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free