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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 2

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

Fortuné Massamba(University of KwaZulu-Natal)0000-0002-6922-3566
Samuel Ssekajja(University of KwaZulu-Natal)0000-0003-4247-1989
Pages
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Publication Date
2020-04-02
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Sahin, Differential geometry of lightlike submanifolds, Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2010].

📌 3 Key Takeaways

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Objective & Hypothesis: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 $\overline{M}^{n+3}$.
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Key Findings & Data: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.
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Conclusion & Impact:Sahin, Differential geometry of lightlike submanifolds, Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2010].
🔬Design:Research Article
📍Scope:2010 Verileri
⚙️Variables:Half-lightlike submanifold · Newton transformation · foliation and mean curvature

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].

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Cite This Article

Massamba, F., Ssekajja, S. (2020). On total mean curvatures of foliated half-lightlike submanifolds in semi-Riemannian manifolds. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 2. https://doi.org/10.15672/hujms.621536

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