Introduction

In this paper we consider de Sitter space, which is a Lorentzian space form with positive curvature defined by a pseudo n-sphere in Minkowski space. The spacelike curves in de Sitter 3-space are investigated in [5] and the lightlike surface of the spacelike curves are constructed from the Frenet-Serret type formula. In [9] the differential geometry of the timelike surfaces in de Sitter space are discussed, and the singularities of de Sitter Gauss images of timelike surfaces in de Sitter 3-space are classified. The principal, asymptotic and characteristic curves associated to the de Sitter Gauss maps are investigated in [10], and the contact of timelike surfaces with geodesic loci are investigated in [11]. In [12] we investigated the lightcone Gauss image of spacelike hypersurface in de Sitter space, which is the analogous tool in [6]. The singularities of the Gauss images correspond to the parabolic sets of spacelike hypersurfaces.