  In this paper we discuss the path integral representations for the coordinate
systems on the complex sphere S3C. The Schroedinger equation, respectively the
path integral, separates in exactly 21 orthogonal coordinate systems. We
enumerate these coordinate systems and we are able to present the path integral
representations explicitly in the majority of the cases. In each solution the
expansion into the wave-functions is stated. Also, the kernel and the
corresponding Green function can be stated in closed form in terms of the
invariant distance on the sphere, respectively on the hyperboloid.
