Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four Darboux spaces of revolution that have at least two integrals of motion quadratic in the momenta, in addition to the Hamiltonian. These are two-dimensional spaces of nonconstant curvature. It turns out that all of these potentials are equivalent to superintegrable potentials in complex Euclidean 2-space or on the complex 2-sphere, via ``coupling constant metamorphosis'' (or equivalently, via Stäckel multiplier transformations). We present tables of the results.
Institute for Mathematics and Its Applications>IMA Preprints Series
Kalnins, E.G.; Kress, J.M.; Miller, Jr., W.; Winternitz, P..
Superintegrable systems in Darboux spaces.
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