Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2

@article{Cariena2005CentralPO,
  title={Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2},
  author={Jos{\'e} F. Cari{\~n}ena and Manuel F Ra{\~n}ada and Mariano Santander},
  journal={Journal of Mathematical Physics},
  year={2005},
  volume={46},
  pages={052702}
}
The Kepler problem is a dynamical system that is well defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane. First, the theory of central potentials on spaces of constant curvature is studied. All the mathematical expressions are presented using the curvature κ as a parameter, in such a way that they reduce to the appropriate property for the system on the sphere S2, or on the hyperbolic plane H2, when particularized for κ>0, or κ<0, respectively; in… 
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