Foliations by spacelike hypersurfaces on Lorentz manifolds

Abstract

In this work we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We find an equation that relates the foliation with the ambient manifold and apply it to investigate conditions for the leaves being totally umbilical or geodesic. Using the Maximum principle with the mentioned equation we obtain an obstruction for the existence of totally geodesic spacelike foliations in a spacetime with positive Ricci curvature on the direction N