Lightlike Hypersurfaces and Canal Hypersurfaces of Lorentzian Surfaces

Abstract

The lightlike hypersurfaces in semi-Euclidean space are of special interest in Relativity Theory. In particular, the singularities of these lightlike hypersurfaces provide good models for the study of different horizon types. And we obtain some geometrical propositions of the canal hypersurfaces of Lorentzian surfaces. We introduce the notions of flatness for these hypersurfaces and study their singularities.