Lobachevskii Journal of Mathematics

, Volume 34, Issue 1, pp 76–84 | Cite as

Integrability of distributions in GCR-lightlike submanifolds of indefinite cosymplectic manifolds

Article
  • 98 Downloads

Abstract

We give necessary and sufficient conditions for the integrability of various distributions of GCR-lightlike submanifold of an indefinite Cosymplectic manifold.We also find the conditions for each leaf of holomorphic distribution and radical distribution to be totally geodesic in submanifold.

Keywords and phrases

Indefinite Cosymplectic manifolds lightlike submanifolds GCRlightlike submanifolds 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Bejancu, Geometry of CR-Submanifolds (Kluwer Academic Publishers, 1986).MATHCrossRefGoogle Scholar
  2. 2.
    D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds (Birkhauser, 2002).MATHGoogle Scholar
  3. 3.
    C. Calin, Arab Journal of Mathematical Sciences 5, 21 (1999).MathSciNetMATHGoogle Scholar
  4. 4.
    K. L. Duggal and A. Bejancu, Lightlike Submanifolds of semi-Riemannian Manifolds and Applications (Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996).MATHCrossRefGoogle Scholar
  5. 5.
    K. L. Duggal and B. Sahin, Acta Math. Hungar 106, 125 (2005).MathSciNetCrossRefGoogle Scholar
  6. 6.
    K. L. Duggal and B. Sahin, Acta Math. Hungar 112, 107 (2006).MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    K. L. Duggal and B. Sahin, IJMMS, Article ID 57585 (2007).Google Scholar
  8. 8.
    K. L. Duggal and B. Sahin, Acta Math. Hungar 122, 45 (2009).MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Sangeet Kumar, Rakesh Kumar and R. K. Nagaich, Integrebility of Distributions in GCR-lightlike Submanifolds of Indefinite Kaehler Manifolds, Commun. Korean Math. Soc. 27(3), 591–602 (2012).MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    K. Yano and M. Kon, CR Submanifolds of Kaehlerian and Sasakian Manifolds (Birkhauser, Boston, 1983).MATHCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • Varun Jain
    • 1
  • Rakesh Kumar
    • 2
  • Rakesh Kumar Nagaich
    • 3
  1. 1.Multani Mal Modi CollegePatialaIndia
  2. 2.University College of EngineeringPunjabi UniversityPatialaIndia
  3. 3.Department of MathematicsPunjabi UniversityPatialaIndia

Personalised recommendations