Explicit metrics for a class of two-dimensional cubically superintegrable systems

被引：12

作者：

Valent, Galliano ^{[1
,2
,3
,4
]}

Duval, Christian ^{[3
,4
]}

Shevchishin, Vsevolod ^{[5
]}

机构：

[1] Univ Paris 06, Sorbonne Univ, UMR 7589, LPTHE, F-75005 Paris, France

[2] CNRS, UMR 7589, LPTHE, F-75005 Paris, France

[3] Aix Marseille Univ, CNRS UMR 7332, CPT, F-13288 Marseille, France

[4] Univ Toulon & Var, CNRS UMR 7332, CPT, F-83957 La Garde, France

[5] Natl Res Univ, Fac Math, Higher Sch Econ, Moscow, Russia

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2015年 / 87卷

关键词：

Superintegrable Hamiltonian systems; Polynomially integrable Riemannian metrics on surfaces; Globally integrable Riemannian metrics on surfaces; Completely integrable systems on the 2-sphere; INTEGRABLE SYSTEMS;

D O I：

10.1016/j.geomphys.2014.08.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain, in local coordinates, the explicit form of the two-dimensional, superintegrable systems of Matveev and Shevchishin involving linear and cubic integrals. This enables us to determine for which values of the parameters these systems are indeed globally defined on S-2. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：461 / 481

页数：21

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