Skip to main content
SpringerLink
Log in

Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold

  • Published:
Indian Journal of Pure and Applied Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we study the geometry of lightlike hypersurfaces of an indefinite Sasakian manifold. The main result is to prove three characterization theorems for such a lightlike hypersurface. In addition to these main theorems, we study the geometry of totally geodesic lightlike hypersurfaces of an indefinite Sasakian manifold.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C. Atindogbe and K. L. Duggal, Conformal screen on lightlike hypersurfaces, International J. of Pure and Applied Math., 11(4) (2004), 421–442.

    MATH  MathSciNet  Google Scholar 

  2. C. Călin, Contributions to geometry of CR-submanifold, Thesis, University of Iasi (Romania, 1998).

    Google Scholar 

  3. B. Y. Chen, Geometry of Submanifolds, Marcel Dekker, New York, 1973.

    MATH  Google Scholar 

  4. K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996.

    MATH  Google Scholar 

  5. K. L. Duggal and D. H. Jin, Null curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.

  6. K. L. Duggal and D. H. Jin, A classification of Einstein lightlike hypersurfaces of a Lorentzian space form, to appear in J. Geom. Phys.

  7. K. L. Duggal and B. Sahin, Lightlike Submanifolds of indefinite Sasakian manifolds, Int. J. Math. and Math. Sci., 2007, Art. ID 57585, 21 pages, Doi:10.1155/2007/57585.

  8. K. L. Duggal and B. Sahin, Generalized Cauchy-Riemann lightlike Submanifolds of indefinite Sasakian manifolds, Acta Math. Hungar., 2008, DOI:10.1007/ s10474-008-7221-8.

  9. D. H. Jin, Screen conformal lightlike hypersurfaces of a semi-Riemannian space form, J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math., 16(3), (2009), 271–276.

    MathSciNet  Google Scholar 

  10. D. H. Jin, Lightlike hypersurfaces with totally umbilical screen distributions, Chungcheong Math. Soc., 22(3), 2009, 409–416.

    Google Scholar 

  11. D. H. Jin, Screen conformal lightlike real hypersurfaces of an indefinite complex space form, Bull. Korean Math. Soc., 2009, 341–353.

  12. D. H. Jin, Lightlike real hypersurfaces with totally umbilical screen distributions, Commun. Korean Math. Soc., 2009, 225–234.

  13. T. H. Kang, S. D. Jung, B. H. Kim, H. K. Pak and J. S. Pak, Lightlike hypersurfaces of indefinite Sasakian manifolds, Indian J. Pure and Appl., Math., 34 (2003), 1369–1380.

    MATH  MathSciNet  Google Scholar 

  14. B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983.

  15. T. Takahashi, Sasakian manifolds with pseudo-Riemannian metric, Tôhoku Math. J., 21 (1969), 271–290.

    Article  MATH  Google Scholar 

  16. S. Tanno, Sasakian manifolds with constant J-holomorphic sectional curvature, Tôhoku Math. J., 21 (1969), 501–507.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Dongguk University, Kyongju, 780-714, Korea

    D. H. Jin

Authors
  1. D. H. Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. H. Jin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jin, D.H. Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold. Indian J Pure Appl Math 41, 569–581 (2010). https://doi.org/10.1007/s13226-010-0032-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13226-010-0032-y

Key words

Search

Navigation