New superintegrable models with position-dependent mass from Bertrand's Theorem on curved spaces

@article{Ballesteros2011NewSM,
  title={New superintegrable models with position-dependent mass from Bertrand's Theorem on curved spaces},
  author={{\'A}ngel Ballesteros and Alberto Enciso and Francisco J. Herranz and Orlando Ragnisco and Danilo Riglioni},
  journal={Journal of Physics: Conference Series},
  year={2011},
  volume={284},
  pages={012011}
}
A generalized version of Bertrand's theorem on spherically symmetric curved spaces is presented. This result is based on the classification of (3+1)-dimensional (Lorentzian) Bertrand spacetimes, that gives rise to two families of Hamiltonian systems defined on certain 3-dimensional (Riemannian) spaces. These two systems are shown to be either the Kepler or the oscillator potentials on the corresponding Bertrand spaces, and both of them are maximally superintegrable. Afterwards, the relationship… 

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