SCREEN SEMI-INVARYANT HALF-LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN PRODUCT MANIFOLD WITH QUARTER-SYMMETRIC CONNECTION

Year 2016, Volume: 4 Issue: 2, 271 - 281, 01.10.2016

Oğuzhan Bahadır

Abstract

In this paper, we study half-lightlike submanifolds of a semi- Riemannian product manifold. We introduce a classes half-lightlike subman- ifolds of called screen semi-invariant half-lightlike submanifolds. We de ned some special distribution of screen semi-invariant half-lightlike submanifold. We give some equivalent conditions for integrability of distributions with re- spect to the Levi-Civita connection of semi-Riemannian manifolds and quarter- symmetric non-metric connection of semi-Riemannian manifolds and some re- sults.

Keywords

Half-lightlike submanifold, Product manifolds, Screen semi-invariant, Quarter-symmetric connection

References

• [1] H. A. Hayden, Sub-spaces of a space with torsion, Proceedings of the London Mathematical Society, vol. 34, 1932, 2750.
• [2] K.Yano, On semi-symmetric metric connections, Rev. Roumania Math. Pures Appl. 15, 1970 , 1579-1586.
• [3] S.Golab, On semi-symmetric metric and quarter-symmetric linear connections, Tensor 29, 1975, 249-254.
• [4] N, S. Agashe and M, R, Cha e, A semi symetric non-metric connection in a Riemannian manifold, Indian J. Pure Appl. Math. 23, 1992, 399-409
• [5] B.B. Chaturvedi and P. N. Pandey, Semi-symetric non metric connections on a Kahler Man- ifold, Diferantial Geometry-Dinamical Systems, 10, 2008, 86-90
• [6] M. M. Tripathi, A new connection in a Riemannian manifold, International Journal of Geo. 1, 2008, 15-24.
• [7] Duggal, Krishan L. and Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publishers, Dordrecht, 1996.
• [8] Duggal, K. L. and Bejancu, A. Lightlike submanifolds of codimension two, Math. J. Toyama Univ., 15(1992), 59{82.
• [9] Duggal, K.L. and Jin, D.H.: Null Curves and Hypersurfaces of Semi-Riemannian manifolds, World Scientic Publishing Co. Pte. Ltd., 2007.
• [10] Duggal, K. L. Riemannian geometry of half lightlike submanifolds, Math. J. Toyama Univ., 25, (2002), 169{179.
• [11] Duggal, K. L. and Sahin, B. Screen conformal half-lightlike submanifolds, Int.. J. Math., Math. Sci., 68, (2004), 3737{3753.
• [12] Duggal, K. L. and Sahin, B. Screen Cauchy Riemann lightlike submanifolds, Acta Math. Hungar., 106(1-2) (2005), 137{165
• [13] Duggal, K. L. and Sahin, B. Generalized Cauchy Riemann lightlike submanifolds, Acta Math. Hungar., 112(1-2), (2006), 113{136.
• [14] Duggal, K. L. and Sahin, B. Lightlike submanifolds of indenite Sasakian manifolds, Int. J. Math. Math. Sci., 2007, Art ID 57585, 1{21.[162]
• [15] Duggal, K. L. and Sahin, B. Contact generalized CR-lightlike submanifolds of Sasakian sub- manifolds. Acta Math. Hungar., 122, No. 1-2, (2009), 45{58.
• [16] Atceken, M. and Kilic, E., Semi-Invariant Lightlike Submanifolds of a Semi- Riemannian Product Manifold, Kodai Math. J., Vol. 30, No. 3, (2007), pp. 361-378.
• [17] Duggal K. L., Sahin B., Dierential Geometry of Lightlike Submanifolds, Birkhauser Veriag AG Basel-Boston-Berlin (2010).
• [18] Kilic, E. and Sahin, B., Radical Anti-Invariant Lightlike Submanifolds of a Semi-Riemannian Product Manifold, Turkish J. Math., 32, (2008), 429-449.
• [19] Kilic, E. and Bahadir, O., Lightlike Hypersurfaces of a Semi-Riemannian Product Manifold and Quarter-Symmetric Nonmetric Connections, Hindawi Publishing Corporation Interna- tional Journal of Mathematics and Mathematical Sciences Volume 2012, Article ID 178390, 17 pages.
• [20] Bahadir, O., Screen Semi invariant Half-Lightlike submanifolds of a Semi-Riemannian Prod- uct Manifold, Global Journal of Advanced Research on Classical and Modern Geometries, ISSN: 2284-5569, Vol4, (2015) Issue 2, pp.116-124