Time-like hypersurfaces in de Sitter space and Legendrian singularities

Abstract

We construct a basic framework for studying the extrinsic differential geometry on time-like hypersurfaces in the de Sitter space from the viewpoint of the theory of Legendrian singularities. As an application, we study the contact of time-like hypersurfaces with flat totally umbilic time-like hypersurfaces in the de Sitter space. © Springer Science+Business Media, Inc. 2007.