Subvariedades aprisionadas compactas do tipo-espaço com codimensão 2 através das hipersuperfícies especiais do espaco-tempo de Sitter

Abstract

In this work, we study the obtainment of compact submanifolds of the codimension 2 spacelike through special lightlike hypersurfaces. For a more in-depth understanding, we will approach from the main results of Riemannian and semi-Riemannian geometries. We will see that obtaining a temporal orientation for the Lorentzian submanifolds Σ and a pseudo-orthogonal basis for (TΣ)⊥ have the fundamental feature for our calculation base and, thus, we can define and to characterize the trapped submanifolds as to their causality and inform which restrictions are necessary to be considered compact.