Research Article
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Year 2016, Volume: 9 Issue: 1, 9 - 22, 30.04.2016
https://doi.org/10.36890/iejg.591880

Abstract

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

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

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.

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
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Oğuzhan Bahadır

Erol Kılıç

Publication Date April 30, 2016
Published in Issue Year 2016 Volume: 9 Issue: 1

Cite

APA Bahadır, O., & Kılıç, E. (2016). Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection. International Electronic Journal of Geometry, 9(1), 9-22. https://doi.org/10.36890/iejg.591880
AMA Bahadır O, Kılıç E. Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection. Int. Electron. J. Geom. April 2016;9(1):9-22. doi:10.36890/iejg.591880
Chicago Bahadır, Oğuzhan, and Erol Kılıç. “Lightlike Submanifolds of a Semi-Riemannian Product Manifold With Quarter Symmetric Non-Metric Connection”. International Electronic Journal of Geometry 9, no. 1 (April 2016): 9-22. https://doi.org/10.36890/iejg.591880.
EndNote Bahadır O, Kılıç E (April 1, 2016) Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection. International Electronic Journal of Geometry 9 1 9–22.
IEEE O. Bahadır and E. Kılıç, “Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection”, Int. Electron. J. Geom., vol. 9, no. 1, pp. 9–22, 2016, doi: 10.36890/iejg.591880.
ISNAD Bahadır, Oğuzhan - Kılıç, Erol. “Lightlike Submanifolds of a Semi-Riemannian Product Manifold With Quarter Symmetric Non-Metric Connection”. International Electronic Journal of Geometry 9/1 (April 2016), 9-22. https://doi.org/10.36890/iejg.591880.
JAMA Bahadır O, Kılıç E. Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection. Int. Electron. J. Geom. 2016;9:9–22.
MLA Bahadır, Oğuzhan and Erol Kılıç. “Lightlike Submanifolds of a Semi-Riemannian Product Manifold With Quarter Symmetric Non-Metric Connection”. International Electronic Journal of Geometry, vol. 9, no. 1, 2016, pp. 9-22, doi:10.36890/iejg.591880.
Vancouver Bahadır O, Kılıç E. Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection. Int. Electron. J. Geom. 2016;9(1):9-22.