Abstract: The space-like hypersurfaces with constant scalar curvature in a de Sitter space were studied and a pinching theorem on the square of the norm of the second fundamental form was obtained. This theorem has improved the results obtained by LI Hai-zhong who firstly studied the rigidity problem for a hypersurface with constant scalar curvature by introducing a self-adjoint second order differential operator.

Key words: de Sitter space, space-like hypersurface, scalar curva ture