Completeness of superintegrability in two-dimensional constant curvature spaces
E. G. Kalnins, J. M. Kress, G. S. Pogosyan, W. Miller
Abstract
We classify the Hamiltonians H=px2+py2+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=J12+J22+J32+V(x,y,z) on the complex 2-sphere where x2+y2+z2=1. This is achieved in all generality using properties of the complex Euclidean group and the complex orthogonal group.
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