On total mean curvatures of foliated half-lightlike submanifolds in semi-Riemannian manifolds

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 ${\bar{M}}^{n+3}$. 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].