  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 .
