Hokkaido University Preprint Series in Mathematics
The Lorentzian space form with the positive curvature is called de Sitter space which is an important subject in the theory of relativity. In this paper we consider spacelike curves in de Sitter $3$-space. We define the notion of lightlike surfaces of spacelike curves in de Sitter $3$-space. We investigate the geometric meanings of the singularities of such surfaces.