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Screen Slant Lightlike Submanifolds of Indefinite Sasakian Manifolds

Haider, S.M. Khursheed;Advin, Advin;Thakur, Mamta

  • Received : 2010.12.08
  • Accepted : 2012.10.09
  • Published : 2012.12.23

Abstract

In this paper, we introduce screen slant lightlike submanifold of an indefinite Sasakian manifold and give examples. We prove a characterization theorem for the existence of screen slant lightlike submanifolds. We also obtain integrability conditions of both screen and radical distributions, prove characterization theorems on the existence of minimal screen slant lightlike submanifolds and give an example of proper minimal screen slant lightlike submanifolds of $R_2^9$.

Keywords

Degenerate metric;screen slant lightlike submanifold;indefinite Sasakian manifold

References

  1. C. L. Bejan and K. L. Duggal, Global lightlike manifolds and harmonicity, Kodai Math. J., 28(1)(2005), 131-145. https://doi.org/10.2996/kmj/1111588042
  2. B. Y. Chen, Slant immersion, Bull. Aust. Math. Soc., 41(1990), 135-147. https://doi.org/10.1017/S0004972700017925
  3. K. L. Duggal, Spacetime manifolds and contact structures, Internat. J Math. & Math. Sci., 13(1990), 545-554. https://doi.org/10.1155/S0161171290000783
  4. K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics, Birkhauser, 2010.
  5. K. L. Duggal and B. Sahin, Screen Cauchy-Riemannian lightlike submanifolds, Acta Math. Hungar., 106(1-2)(2005), 137-165. https://doi.org/10.1007/s10474-005-0011-7
  6. K. L. Duggal and B. Sahin, Lightlike submanifolds of indefinite Sasakian manifolds, Internat. J. Math. & Math. Sci., 2007(2007), Article ID 57585, 21 pages.
  7. D. N. Kupeli, Singular Semi-Riemannian Geometry, Kluwer Dortrecht,(1996).
  8. A. Lotta, Slant submanifolds in contact geometry, Bull. Math.Soc. Roumania, 39(1996), 183-198.
  9. B. O' Neill, Semi-Riemannian Geometry with Applications to Relativity, Pure And Applied Math. Academic Press, New York, 1982.
  10. B. Sahin, Slant lightlike submanifolds of indefinite Hermitian manifolds, Balkan J. Geometry And Its Applications, 13(2008), 107-119.
  11. B. Sahin, Screen slant lightlike submanifolds, Int. Electron. J. Geom., 2(1)(2009), 41-54.
  12. B. Sahin and C. Yildirim, Slant lightlike submanifolds of indefinite Sasakian manifolds, Filomat, 26:2(2012), 71-81.
  13. T. Takahashi, Sasakian manifolds with pseudo-Riemannian metric, Tohoku Math.j., 21(1969), 271-290. https://doi.org/10.2748/tmj/1178242996
  14. K. Yano and M. Kon, Structures on Manifolds, World Scientific, Singapore, 1984.

Cited by

  1. Screen Pseudo-Slant Lightlike Submanifolds of Indefinite Sasakian Manifolds vol.13, pp.2, 2016, https://doi.org/10.1007/s00009-015-0526-2