E G Kalnins et al 2001 J. Phys. A: Math. Gen. 34 4705 doi:10.1088/0305-4470/34/22/311
Completeness of superintegrability in two-dimensional constant-curvature spaces
E G Kalnins1, J M Kress1, G S Pogosyan2,4 and W Miller Jr3
Show affiliationsWe classify the Hamiltonians H = px2 + py2 + V(x,y) of all classical superintegrable systems in two-dimensional complex Euclidean space with two additional second-order constants of the motion. We similarly classify the superintegrable Hamiltonians H = J12 + J22 + J32 + V(x, y, z) on the complex two-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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Issue 22 (8 June 2001)
Received 7 February 2001
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Completeness of superintegrability in two-dimensional constant-curvature spaces
E G Kalnins et al 2001 J. Phys. A: Math. Gen. 34 4705
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