ON COMPLETE TOTALLY UMBILICAL AND MAXIMAL SPACE-LIKE SURFACES IN PSEUDO-RIEMANNIAN MANIFOLDS.

Space-like surfaces with special second fundamental forms have been an important tool in the study of pseudo-Riemannian manifolds. This paper focuses on adapting some theorems of Riemannian geometry in the large to the study of geometry of space-like surfaces of pseudo-Riemannian manifolds, specifically, various comparison theorems that use sectional and Ricci curvatures. The purpose of this paper is to establish a global geometry of complete spacelike totally umbilical and maximal surfaces in pseudo-Riemannian manifolds. [ABSTRACT FROM AUTHOR]