Abstract
We explicitly construct compact conformally flat hypersurfaces in a simply connected, (n+1)-dimensional space form, where n is greater than 3. We may assume that the ambient space is the standard (n+1)-sphere by a conformal diffeomorphism of a simply connected space form into the sphere. From this viewpoint we give a global parameterization of compact conformally flat hypersurfaces, and we establish relation between two types of hypersurfaces; one has umbilic points and the other has not. It is known that each compact conformally flat hypersurface in a space form is conformally equivalent to a classical Schottky manifold. In order to determine the conformal types of our hypersurfaces, we explicitly represent conformal diffeomorphism of these hypersurfaces to corresponding Schottky manifolds. In particular, we clarify the relation between our results and Pinkall's results.
