The Structure of Minimizing Hypersurfaces Mod 4.
In this paper we study the topological and metric rigidity of hypersurfaces in , the -dimensional hyperbolic space of sectional curvature . We find conditions to ensure a complete connected oriented hypersurface in to be diffeomorphic to a Euclidean sphere. We also give sufficient conditions for a complete connected oriented closed hypersurface with constant norm of the second fundamental form to be totally umbilic.
This paper is a survey of results on topological structures and curvature structures of complete submanifolds in a Euclidean space.