Spacelike hypersurfaces in de Sitter space with constant higher-order mean curvature

摘要

The authors apply the generalized Minkowski formula to set up aspherical theorem. It is shown that a compact connectedhypersurface with positive constant higher-order mean curvatureHrfor some fixedr,1≤r≤n, immersed in the deSitter spaceS1n+1must be a sphere.