Superintegrability on the three-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the sphere S 3 and on the hyperbolic space H 3

  title={Superintegrability on the three-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the sphere S 3 and on the hyperbolic space H 3},
  author={Jos{\'e} F. Cari{\~n}ena and Manuel F Ra{\~n}ada and Mariano Santander},
  journal={Journal of Physics A: Mathematical and Theoretical},
The superintegrability of several Hamiltonian systems defined on three-dimensional configuration spaces of constant curvature is studied. We first analyze the properties of the Killing vector fields, Noether symmetries and Noether momenta. Then we study the superintegrability of the harmonic oscillator, the Smorodinsky–Winternitz system and the harmonic oscillator with ratio of frequencies 1:1:2 and additional nonlinear terms on the three-dimensional sphere S 3 (κ > 0) and on the hyperbolic… 
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