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Dergiler / 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
Sayfa
727–739
Yayın Tarihi
2022-10-18
DOI
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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:Araştırma Makalesi
📍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

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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Kaynakça (11)

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  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
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  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.