Resultados de rigidez e não existência para subvariedades trapped em espaços Lorentzianos

Abstract

In this work, we study marginally trapped and weakly trapped submanifolds immersed in generalized Robertson-Walker (GRW) spacetime, and we obtain some rigity results that, under appropriate hypothesis, guarantee that such submanifolds are contained in slices. We also get non-existence results for weakly trapped submanifolds immersed in such spaces, and some applications for cases of physical relevance. After, we study trapped and marginally trapped submanifolds immersed in a Lorentzian space form (Fórmula), with constant sectional curvature c. In this sense, we establish sufficient conditions to guarantee that a complete trapped submanifolds with parallel mean curvature vector of (Fórmula) must be pseudo-umbilical, we obtain a non-existence result for trapped submanifolds in the Minkowski space, and finally, we establish sufficient conditions to guarantee that a complete pseudo-umbilical marginally trapped submanifolds of (Fórmula) with parallel mean curvature vector must be totally umbilical.