Nonintegrability of the two-body problem in constant curvature spaces II
  We consider the reduced two-body problem with a central potential on the sphere ${\bf S}^{2}$ and the hyperbolic plane ${\bf H}^{2}$. For two potentials different from the Newton and the oscillator ones we prove the nonexistence of an additional meromorphic integral for the complexified dynamic systems. 
Alexey V. Shchepetilov