Superintegrability in a two-dimensional space of nonconstant curvature

@article{Kalnins2002SuperintegrabilityIA,
  title={Superintegrability in a two-dimensional space of nonconstant curvature},
  author={Ernest G. Kalnins and Jonathan M. Kress and Pavel Winternitz},
  journal={Journal of Mathematical Physics},
  year={2002},
  volume={43},
  pages={970-983}
}
A Hamiltonian with two degrees of freedom is said to be superintegrable if it admits three functionally independent integrals of the motion. This property has been extensively studied in the case of two-dimensional spaces of constant (possibly zero) curvature when all the independent integrals are either quadratic or linear in the canonical momenta. In this article the first steps are taken to solve the problem of superintegrability of this type on an arbitrary curved manifold in two dimensions… 
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