paper

Completeness of superintegrability in two-dimensional constant curvature spaces

arXiv:math-ph/0102006 · doi:10.1088/0305-4470/34/22/311

Abstract

We classify the Hamiltonians $H = p_{x}^{2} + p_{y}^{2} + V (x, y)$ of all classical superintegrable systems in two dimensional complex Euclidean space with second-order constants of the motion. We similarly classify the superintegrable Hamiltonians $H = J_{1}^{2} + J_{2}^{2} + J_{3}^{2} + V (x, y, z)$ on the complex 2-sphere where $x^{2} + y^{2} + z^{2} = 1$ . This is achieved in all generality using properties of the complex Euclidean group and the complex orthogonal group.

23 pages, LaTeX