Curvature properties of compact spacelike hypersurfaces in de Sitter space

In this paper we establish a sufficient condition for a compact spacelike hypersurface in de Sitter space to be spherical in terms of a lower bound for the square of its mean curvature. Our result will be a consequence of the maximum principle for the Laplacian operator. We also derive some other applications and consequences of our main result. In particular, we establish another sufficient condition for a compact spacelike hypersurface in de Sitter space to be spherical in terms of a pinching condition for its scalar curvature, as well as in terms of the Ricci curvature and in terms of the higher order mean curvatures