New characterizations of spacelike hyperplanes in the steady state space

In this article, we deal with complete spacelike hypersurfaces immersed in an open region of the de Sitter space Sn+11 which is known as the steady state space Hn+1. Under suitable constraints on the behavior of the higher order mean curvatures of these hypersurfaces, we are able to prove that they must be spacelike hyperplanes of Hn+1. Furthermore, through the analysis of the hyperbolic cylinders of Hn+1, we discuss the importance of the main hypothesis in our results. Our approach is based on a generalized maximum principle at infinity for complete Riemannian manifolds.