  In this contribution a path integral approach for the quantum motion on
three-dimensional spaces according to Koenigs, for short``Koenigs-Spaces'', is
discussed. Their construction is simple: One takes a Hamiltonian from
three-dimensional flat space and divides it by a three-dimensional
superintegrable potential. Such superintegrable potentials will be the
isotropic singular oscillator, the Holt-potential, the Coulomb potential, or
two centrifugal potentials, respectively. In all cases a non-trivial space of
non-constant curvature is generated. In order to obtain a proper quantum theory
a curvature term has to be incorporated into the quantum Hamiltonian. For
possible bound-state solutions we find equations up to twelfth order in the
energy E.
