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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 5

Pseudo-totally umbilical lightlike submanifolds

Samuel Ssekajja(University of the Witwatersrand)0000-0003-4247-1989
Pages
—
Publication Date
2022-10-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we introduce the notion of mean lightlike sectional curvatures and relate them to the well-known tensors used in the characterisation of lightlike hypersurfaces in space-times.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We introduce the geometry of pseudo-totally umbilical lightlike submanifold $M$ of a semi-Riemannian manifold $\bar{M}$.
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Key Findings & Data:In line with the above, we give a complete classification of pseudo-totally umbilical $1$-lightlike submanifolds, such as the lightlike hypersurfaces and half-lightlike submanifolds.
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Conclusion & Impact:Finally, we introduce the notion of mean lightlike sectional curvatures and relate them to the well-known tensors used in the characterisation of lightlike hypersurfaces in space-times.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:lightlike submanifolds · pseudo-totally umbilical submanifolds · mean lightlike sectional curvatures

Abstract

We introduce the geometry of pseudo-totally umbilical lightlike submanifold $M$ of a semi-Riemannian manifold $\bar{M}$. In line with the above, we give a complete classification of pseudo-totally umbilical $1$-lightlike submanifolds, such as the lightlike hypersurfaces and half-lightlike submanifolds. Furthermore, pseudo-totally umbilical screen distributions are also investigated, with a complete classification for any lightlike hypersurfaces whose screen distributions are pseudo-totally umbilical. Closely linked to the above we also show, under some geometric conditions, that some pseudo-totally umbilical leaves $M^{*}$, of the screen distribution over $M$, as non-degenerate submanifolds of $\bar{M}$, are either contained in semi-Euclidean spheres or the hyperbolic spaces. Moreover, tangible examples are constructed in this case. Finally, we introduce the notion of mean lightlike sectional curvatures and relate them to the well-known tensors used in the characterisation of lightlike hypersurfaces in space-times.

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Cite This Article

Ssekajja, S. (2022). Pseudo-totally umbilical lightlike submanifolds. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 5. https://doi.org/10.15672/hujms.932487

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