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Completeness of superintegrability in two-dimensional constant curvature spaces

E. G. Kalnins·J. M. Kress·G. S. Pogosyan·W. Miller Jr
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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.

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E. G. Kalnins, J. M. Kress, G. S. Pogosyan, W. Miller Jr. 2001-02-07. Completeness of superintegrability in two-dimensional constant curvature spaces. https://doi.org/10.1088/0305-4470%2F34%2F22%2F311

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