Path integral approach for superintegrable potentials on the three-dimensional hyperboloid

In the present paper on super integrable potentials on spaces of constant curvature we discuss the case of the three-dimensional hyperboloid. Whereas in many coordinate systems an explicit path integral solution for the corresponding potential is impossible, we list in the soluble cases the path integral solutions explicitly in terms of the propagators and the spectral expansions into the wave-functions. We find the analogues of the maximally and minimally superintegrable potentials of IR3 on the hyperboloid and many minimally super integrable potentials which emerge from the subgroup chains corresponding to SO(3, 1). Some special care is taken for the proper generalization of the harmonic oscillator and the Kepler problem