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

Abstract

In this paper we develop Minkowski-type formulae for compact spacelike immersed hypersurfaces with boundary and having some constant higher order mean curvature in de Sitter space S 1 n + 1 . We apply them to establish a relation between the mean curvature and the geometry of the boundary, when it is a geodesic sphere contained into a horizontal hyperplane of the steady state space H n + 1 ⊂ S 1 n + 1 .