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

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 S1n+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  Hn+1⊂S1n+1.