In this paper,we study the compact spacelike submanifolds in the de Sitter space,under the assumption that the normalized mean curvature vector is parallel in the normal bundle.Using the generalized Cheng-Yau＇s differential operator,we obtain some general rigidity theorems which naturally generalize some existing results.
Under the assumption that the normalized mean curvature vector is parallel in the normal bundle, by using the generalized ChengYau＇s self-adjoint differential operator, here we obtain some rigidity results for compact submanifolds with constant scalar curvature and higher codimension in the space forms.
