On complete spacelike hypersurfaces with two distinct principal curvatures in a de Sitter space

We investigate complete spacelike hypersurfaces in a de Sitter space with two distinct principal curvatures and constant m-th mean curvature. By using Otsuki's idea, we obtain some global classification results. As their applications, we obtain some characterizations for hyperbolic cylinders. We prove that the only complete spacelike hypersurfaces in de Sitter (n + 1)-spaces S(1)(n+1)(1) (n >= 3) of constant m-th mean curvature H(m)(|H(m)| >= 1) with two distinct principal curvatures lambda and mu satisfying inf(lambda - mu)(2) > 0 are the hyperbolic cylinders. We also obtain some global rigidity results for hyperbolic cylinders and obtain some non-existence results. (C) 2011 Elsevier B.V. All rights reserved.