Curvature properties of compact spacelike hypersurfaces in de Sitter space (Q5936470)

The authors find a sufficient condition for a compact spacelike hypersurface in de Sitter space to be spherical. The condition is given in terms of a lower bound for the square of its mean curvature. As applications of this result, the authors obtain sufficient conditions for a compact spacelike hypersurface in de Sitter space to be spherical. These conditions are given in terms of a pinching condition for its scalar curvature, as well as in terms of the Ricci curvature and in terms of higher order mean curvatures.