Complete spacelike hypersurfaces in a de Sitter space

In this paper, we characterise the n-dimensional (n >= 3) complete spacelike hypersurfaces M-n in a de Sitter space S-1(n+1) with constant scalar curvature and with two distinct principal curvatures. We show that if the multiplicities of such principal curvatures are greater than 1, then M-n is isometric to H-k(sinh r) x Sn-k(cosh r), 1 < k < n - 1. In particular, when M-n is the complete spacelike hypersurfaces in S-1(n+1) with the scalar curvature and the mean curvature being linearly related, we also obtain a characteristic Theorem of such hypersurfaces.