Complete Spacelike Submanifolds in de Sitter Space with Parallel Mean Curvature Vector Satisfying

Recently, Montiel (7) proved that an -dimensional ( 3) complete spacelike hyper- surface in de Sitter space 1 1 1 with constant mean curvature satisfying 2 4 1 2 which is not connected at infinity must be, up to rigidity motion, a certain hyperbolic cylinder. In this paper, we prove that Montiel's result still holds for higher codimensional spacelike submanifolds in de Sitter space 1 .