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

TL;DR

This paper derives formulas for total mean curvatures of specific foliations on half-lightlike submanifolds in semi-Riemannian manifolds, extending previous differential equations to more general cases.

Contribution

It introduces generalized total mean curvature formulas and differential equations for totally umbilical half-lightlike submanifolds with screen distributions.

Findings

Derived total mean curvature integration formulas for foliations.

Established generalized differential equations for mean curvatures.

Extended previous results to broader classes of submanifolds.

Abstract

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].