Superintegrable systems in Darboux spaces

E. G. Kalnins, J. M. Kress, W. Miller, P. Winternitz

Research output: Contribution to journalArticlepeer-review

89 Scopus citations


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 a table of the results.

Original languageEnglish (US)
Pages (from-to)5811-5848
Number of pages38
JournalJournal of Mathematical Physics
Issue number12
StatePublished - Dec 2003

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