Skip to main content
Log in

The existence of weakly symmetric and weakly Ricci-symmetric Sasakian manifolds admitting a quarter-symmetric metric connection

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

The object of the present work is to obtain a necessary condition for the existence of weakly symmetric and weakly Ricci-symmetric Sasakian manifolds admitting a quarter-symmetric metric connection.

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

Access this article

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. Nirmala S. Agashe and Mangala R. Chafle, A semi-symmetric non-metric connection on a Riemannian Manifold, Indian J. Pure Appl. Math., 23 (1992), 399–409.

    MathSciNet  MATH  Google Scholar 

  2. D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. No. 509, Springer (1976).

    MATH  Google Scholar 

  3. A. De, On almost pseudo-symmetric manifolds admitting a semi-symmetric non-metric connection, Acta Math. Hungar., 125 (2009), 183–186.

    Article  MathSciNet  MATH  Google Scholar 

  4. U. C. De and A. K. Gazi, On almost pseudo-symmetric manifolds, to appear in Ann. Univ. Sci. Budapest. Eötvös, Sect. Math.

  5. S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor (N.S.), 29 (1975), 249–254.

    MathSciNet  MATH  Google Scholar 

  6. H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc., 34 (1932), 27–50.

    Article  Google Scholar 

  7. R. S. Mishra and S. N. Pandey, On quarter-symmetric metric F-connections, Tensor (N.S.), 34 (1980), 1–7.

    MathSciNet  MATH  Google Scholar 

  8. A. K. Mondal and U. C. De, Some properties of a quarter-symmetric metric connection on a Sasakian manifold, Bull. Math. Analysis Appl., 1 (2009), 99–108.

    MathSciNet  Google Scholar 

  9. S. C. Rastogi, On quarter-symmetric metric connection, C.R. Acad. Sci. Bulgar, 31 (1978), 811–814.

    MathSciNet  MATH  Google Scholar 

  10. S. C. Rastogi, On quarter-symmetric metric connection, Tensor (N.S.), 44 (1987), 133–141.

    MathSciNet  MATH  Google Scholar 

  11. S. Sasaki, Lectures Notes on Almost Contact Manifolds, Part I, Tohoku University (1975).

  12. S. Sular, Some properties of a Kenmotsu manifold with a semi-symmetric metric connection, International Electronic Journal of Geometry, 3 (2010), 24–34.

    MathSciNet  MATH  Google Scholar 

  13. L. Tamássy and T. Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, Colloq. Math. Soc. J. Bolyai, 56 (1992), 663–670.

    Google Scholar 

  14. L. Tamássy and T. Q. Binh, On weak symmetries of Einstein and Sasakian manifolds, Tensor (N.S.), 53 (1993), 140–148.

    MathSciNet  MATH  Google Scholar 

  15. K. Yano, On semi-symmetric connection, Rev. Roumaine Math., Pure Appl. Math., 15 (1970), 1579–1586.

    MATH  Google Scholar 

  16. K. Yano and T. Imai, Quarter-symmetric metric connections and their curvature tensors, Tensor (N.S.), 38 (1982), 13–18.

    MathSciNet  MATH  Google Scholar 

  17. K. Yano and M. Kon, Structures on Manifolds, Series in Pure Mathematics, 3, World Scientific Publishing Co. (Singapore, 1984).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jai Prakash Jaiswal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jaiswal, J.P. The existence of weakly symmetric and weakly Ricci-symmetric Sasakian manifolds admitting a quarter-symmetric metric connection. Acta Math Hung 132, 358–366 (2011). https://doi.org/10.1007/s10474-011-0076-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-011-0076-4

Key words and phrases

2000 Mathematics Subject Classification

Navigation