Lightlike Submanifolds with Planar Normal Section in Semi Riemannian Product Manifolds

Year 2016, Volume: 9 Issue: 1, 70 - 77, 30.04.2016

Feyza Esra Erdoğan , Cumali Yıldırım

https://doi.org/10.36890/iejg.591894

Cited By: 4

Abstract

In the present paper we give conditions for screen semi invariant lightlike submanifolds of a semi-

Riemannian product manifold to have degenerate planar normal sections. Also we give sufficient

and efficient conditions for screen invariant and screen anti invariant lightlike submanifold of a

semi-Riemanniann product manifold to have non-degenerate planar normal sections.

Keywords

Lightlike submanifolds , semi-Riemannian product manifolds , Planar normal section , Screen transversal lightlike submanifolds

References

• [1] Duggal, Krishan L. and S¸ ahin, B., Differential geometry of lightlike submanifolds. Frontiers in Mathematics. Birkháuser Verlag, Basel, 2010. [2] Krishan L. Duggal and Aurel Bejancu. Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications ( Kluwer Academic Publıshers,Vol.364)
• [3] Feyza E. Erdogan, Rı fat Gunes and Bayram Sahin . Half-lightlike submanifold with planar normal sections in R4 Turk. J. Math. Vol.38,(2014), 764-777
• 4] Feyza E. Erdogan, Bayram Sahin and Rıfat Gunes. Lightlike surfaces with planar normal section in minkowski 3-space I˙nt. Electron. J. Geom.. Vol.7, no.1,2014)
• [5] Bang-yen Chen. Classification of Surfaces with Planar Normal Sections. Journal of Geometry Vol.20 (1983) 122-127
• [6] Young Ho Kim. Pseudo-Riemannian Submanifolds with Pointwise Planar Normal Sections. Math. J. Okayama Univ.34 (1992), 249-257
• [7] Mehmet Atceken and Erol Kilic. Semi- invariant lightlike Submanifolds of a semi-Riemannian Product manifold. Kodai Math. J. 30,(2007), 361-378
• [8] Erol Kilic, Bayram Sahin and Sadık Keles. Screen Semi invariant lightlike submanifolds of semi-Riemannian Product manifolds, Int. Electron. J. Geom.Vol.4 No.2, (2011), 120-135
• [9] Rıfat Günes¸, Bayram S¸ ahin and Erol Kılıç. On Lightlike hypersurfaces of a semi-Riemann space form, Turk J.Math. Vol.27(2003), 283-297
• [10] Kadri Arslan, Noktasal düzlemsel normal kesitlerle immersiyonlar, Geometri ABD. Uludağ Ünv. Fen Bilimleri Enstitüsü, Bursa Y.L.Tezi,1988