The Lightlike Hypersurface In De Sitter Space

In this paper,we consider lightlike hypersurface in (m+ 2)-dimensional de Sitter space.We study local differential geometry of lightlike hypersurface in (m+ 2)-dimensional de Sitter space.And we concern some geometric quantities of lightlike surface in 3-dimensional de Sitter space,such as the connection coefficients,the second fundamental form,etc.Finally,we conclude that lightlike surface is totally umbilical.