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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 2

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

Samuel Ssekajja
Fortuné Massamba
Pages
727–739
Publication Date
2022-10-18
DOI
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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

Ssekajja, S., Massamba, F. (2022). On total mean curvatures of foliated half-lightlike submanifolds in semi-Riemannian manifolds. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 2, 727–739. https://ajindex.com/articles/529635

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References (11)

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