TY - JOUR AU - Aquino, CĂ­cero P. AU - Baltazar, Halyson I. AU - de Lima, Henrique F. PY - 2020/03/29 Y2 - 2024/03/29 TI - New characterizations of spacelike hyperplanes in the steady state space JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 126 IS - 1 SE - Articles DO - 10.7146/math.scand.a-117703 UR - https://www.mscand.dk/article/view/117703 SP - 61-72 AB - <p>In this article, we deal with complete spacelike hypersurfaces immersed in an open region of the de Sitter space $\mathbb {S}^{n+1}_{1}$ which is known as the steady state space $\mathcal {H}^{n+1}$. 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 $\mathcal {H}^{n+1}$. Furthermore, through the analysis of the hyperbolic cylinders of $\mathcal {H}^{n+1}$, 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.</p> ER -