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Dergiler / 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
Sayfa
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Yayın Tarihi
2022-10-01
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

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Amaç & Hipotez:We introduce the geometry of pseudo-totally umbilical lightlike submanifold $M$ of a semi-Riemannian manifold $\bar{M}$.
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Temel Bulgular & Veri: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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Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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