Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in De Sitter space

In this paper we give a partially affirmative answer to the following question posed by Haizhong Li: is a complete spacelike hypersurface in De Sitter space S1n+1(c), n⩾3n⩾3, with constant normalized scalar curvature R   satisfying n−2nc⩽R⩽c totally umbilical?