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Dergiler / 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
Sayfa
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Yayın Tarihi
2020-04-02
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Yapay Zeka Hızlı Bakış & Çıkarımlar

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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri: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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Sonuç & Katkı:Sahin, Differential geometry of lightlike submanifolds, Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2010].
🔬Tür:Research Article
📍Kapsam:2010 Verileri
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (11)

  1. K. Andrzejewski, W. Kozlowski and K. Niedzialomski, Generalized Newton transformation and its applications to extrinsic geometry, Asian J. Math. 20 (2), 293–322, 2016.
  2. K. Andrzejewski and Pawel G. Walczak, The Newton transformation and new integral formulae for foliated manifolds, Ann. Glob. Anal. Geom. 37 (2), 103–111, 2010.
  3. C. Calin, Contributions to geometry of CR-submanifold, Ph.D. thesis, University of Iasi (Romania), 1998.
  4. K.L. Duggal and A. Bejancu, Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and Its Applications, Kluwer Academic Publishers, 1996.
  5. K.L. Duggal and B. Sahin, Screen conformal half-lightlike submanifolds, Int. J. Math. Math. Sci. 2004 (68), 3737–3753, 2004.
  6. K.L. Duggal and B. Sahin, Differential geometry of lightlike submanifolds. Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2010.
  7. D.N. Kupeli, Singuler semi-Riemannian geometry, Mathematics and Its Applications, Vol. 366, Kluwer Academic Publishers, 1996.
  8. F. Massamba, Totally contact umbilical lightlike hypersurfaces of indefinite Sasakian manifolds, Kodai Math. J. 31, 338–358, 2008.
  9. F. Massamba, On semi-parallel lightlike hypersurfaces of indefinite Kenmotsu manifolds, J. Geom. 95, 73–89, 2009.
  10. F. Massamba and S. Ssekajja, Some remarks on quasi generalized CR-null geometry in indefinite nearly cosymplectic manifolds, Int. J. Math. Math. Sci. Art. ID 9613182, 10 pp, 2016.
  11. E. Yasar, A.C. Coken, and A. Yucesan, Lightlike hypersurfaces in semi-Riemannian manifold with semi-symmetric non-metric connection, Math. Scand. 102 (2), 253– 264, 2008.