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

Authors : Fortuné MASSAMBA, Samuel SSEKAJJA

Pages : 727-739

Doi:10.15672/hujms.621536

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Publication Date : 2020-04-02

Article Type : Research Paper

Abstract :We derive total mean curvature integration formulas 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 [K. L. Duggal and B. Sahin, Differential geometry of lightlike submanifolds, Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2010].
Keywords : Half lightlike submanifold, Newton transformation, foliation and mean curvature