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 S 1 n + 1 ( c ) with constant k-th mean curvature and two distinct principal curvatures one of which is simple. We obtain some characterizations of the Riemannian product H 1 ( c 1 ) × S n − 1 ( c 2 ) or H n − 1 ( c 1 ) × S 1 ( c 2 ) in the de Sitter space S 1 n + 1 ( c ) .