Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection

Year 2016, Volume: 9 Issue: 1, 9 - 22, 30.04.2016

Oğuzhan Bahadır , Erol Kılıç

https://doi.org/10.36890/iejg.591880

Cited By: 4

Abstract

We study lightlike submanifolds of a semi-Riemannian product manifold. We introduce a class of

lightlike submanifolds called screen semi-invariant lightlike submanifold. We consider lightlike

submanifolds with respect to a quarter symmetric non-metric connection which is determined by

the product structure. We give some equivalent conditions for integrability of distributions with

respect to the Levi-Civita connection of semi-Riemannian manifolds and the quarter-symmetric

nonmetric connection, and we obtain some results.

Keywords

Lightlike submanifolds, Product manifolds, Quarter symmetric connection

References

• [1] Agashe, N. S. and Chafle, M. R., A semi symetric non-metric connection in a Riemannian manifold. Indian J. Pure Appl. Math. 23, 1992, 399-409
• [2] 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.
• [3] Duggal, K. L. and Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Academic Publishers, Dordrecht, 1996.
• [4] Duggal, K. L. and Bejancu, A., Lightlike submanifolds of codimension two. Math. J. Toyama Univ., 15(1992), 59-82.
• [5] Duggal, K. L. and Sahin, B., Screen Cauchy Riemann lightlike submanifolds. Acta Math. Hungar. 106(1-2) (2005), 137-165
• [6] Duggal, K. L. and Sahin, B., Generalized Cauchy Riemann lightlike submanifolds. Acta Math. Hungar., 112(1-2), (2006), 113-136.
• [7] Duggal, K. L. and Sahin, B., Lightlike submanifolds of indefinite Sasakian manifolds. Int. J. Math. Math. Sci. 2007, Art ID 57585, 1-21.[162]
• [8] Duggal, K. L. and Sahin, B., Contact generalized CR-lightlike submanifolds of Sasakian submanifolds. Acta Math. Hungar. 122, No. 1-2, (2009), 45-58.
• [9] Duggal, K. L., Sahin, B., Differential Geometry of Lightlike Submanifolds. Birkhauser Veriag AG Basel-Boston-Berlin (2010).
• [10] Golab, S., On semi-symmetric metric and quarter-symmetric linear connections, Tensor 29, 1975, 249-254.
• [11] Hayden, H. A., Sub-spaces of a space with torsion. Proceedings of the London Mathematical Society. vol. 34, 1932, 27-50.
• [12] Kilic, E. and Sahin, B., Radical Anti-Invariant Lightlike Submanifolds of a Semi-Riemannian Product Manifold. Turkish J. Math. 32, (2008), 429-449.
• [13] Kilic, E. and Bahadir, O., Lightlike Hypersurfaces of a Semi-Riemannian Product Manifold and Quarter-Symmetric Nonmetric Connections. Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2012, Article ID 178390, 17 pages.
• [14] Tripathi, M. M., A new connection in a Riemannian manifold. International Journal of Geo. 1, (2008), 15-24.
• [15] Yano, K., On semi-symmetric metric connections. Rev. Roumania Math. Pures. Appl. 15, (1970), 1579-1586.
• [16] Yano, K., Kon, M., Structures on Manifolds. World Scientific Publishing Co. Pte, Ltd., 1984