The Riemannian product structures of spacelike hypersurfaces with constant k-th mean curvature in the de Sitter spaces

In this paper, we investigate complete spacelike hypersurfaces in the de Sitter space with constant k-th mean curvature and two distinct principal curvatures one of which is simple. We obtain some characterizations of the Riemannian product H1(c1)×Sn−1(c2) or Hn−1(c1)×S1(c2) in the de Sitter space .