Rigidez e inexistência de hipersuperfícies completas tipo espaço no steady state space.

Abstract

In this work, we study and prove some theorems on the rigidity and nonexistence of complete spacelike hypersurfaces immersed in the Steady State Space H n+1. Such space turns out to be an open region of the De Sitter Lorentz manifold Sn+1 1 that is immersed in the Lorentz-Minkowzki space Ln+2. To accomplish our objective, we use a suitable extension of the Omori-Yau’s generalized maximum principle, due to Alías, Impera and Rigoli in (ALÍAS et al., 2012). The assumed geometric conditions on the behavior of the higher order mean curvatures of these complete spacelike hypersurfaces are going to give us rigidity, so that, they will be hyperplanes of H n+1. The nonexistence will be a consequence of some of the rigidity results.