Novas caracterizações para cilindros hiperbólicos em espaços anti de Sitter

Abstract

In this work, we will study complete maximal spacelike hypersurfaces at space anti de Sitter H^(n+1)_1, or constant scalar curvature, or constant Gauss-Kronecker curvature non-zero. Initially, we will assume that these hypersurfaces have constant scalar curvature and Gauss-Kronecker limited curvature. In the second moment, we will work only with the hypothesis that the constant Gauss-Kronecker’s curvature is nonzero. In both situations, we will characterize the hyperbolic cylinder H^m(c_1) × H^(n−m)(c_2 ), 1 ≤ m ≤ n – 1 as the only hypersurfaces with n − 1 principal curvatures with the same signal at each point.