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

Year 2020, Volume: 49 Issue: 2, 727 - 739, 02.04.2020

Fortuné Massamba Samuel Ssekajja

https://doi.org/10.15672/hujms.621536

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

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