  We derive total mean curvature integration formulae of a three co-dimensional
foliation $\mathcal{F}^{n}$ on a screen integrable half-lightlike submanifold,
$M^{n+1}$ in a semi-Riemannian manifold $\overline{M}^{n+3}$. We give
generalized differential equations relating to mean curvatures of a totally
umbilical half-lightlike submanifold admitting a totally umbilical screen
distribution, and show that they are generalizations of those given by [4].
