Maximal superintegrability on N-dimensional curved spaces

@article{Ballesteros2003MaximalSO,
  title={Maximal superintegrability on N-dimensional curved spaces},
  author={Angel Ballesteros and Francisco J. Herranz and Mariano Santander and Teresa Sanz-Gil},
  journal={Journal of Physics A},
  year={2003},
  volume={36}
}
A unified algebraic construction of the classical Smorodinsky–Winternitz systems on the ND sphere, Euclidean and hyperbolic spaces through the Lie groups SO(N + 1), ISO(N) and SO(N, 1) is presented. Firstly, general expressions for the Hamiltonian and its integrals of motion are given in a linear ambient space N+1, and secondly they are expressed in terms of two geodesic coordinate systems on the ND spaces themselves, with an explicit dependence on the curvature as a parameter. On the sphere… 
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