Unicidade de hipersuperfícies tipo-espaço com curvatura média de ordem superior constante em espaço-tempo de Robertson-Walker generalizado

Abstract

We will study, according to Alias ​​and Colares in [11], the uniqueness problem for space-like hypersurfaces with constant higher-order mean curvature in a generalized Robertson-Walker (GRW) spacetime. In particular, we will consider the following question: Under what conditions should a compact space-like hypersurface with constant higher-order mean curvature in a spatially closed GRW spacetime be a space-like slice? We will prove that this essentially occurs under the so-called null convergence condition. Our approach is based on the use of Newton's transformations (and their associated differential operators) and Minkowski's formulas for space-like hypersurfaces.