Lobachevskii Journal of Mathematics

, Volume 37, Issue 2, pp 146–154 | Cite as

Para-Sasakian manifolds satisfying certain curvature conditions

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Abstract

In this paper, we investigate P-Sasakian manifolds satisfying the conditions R(X, ξ) · C = 0 and \(C \cdot \widetilde Z = 0\), where C and \(\widetilde Z\) are the Weyl conformal curvature tensor and the concircular curvature tensor respectively. Next, we study 3-dimensional P-Sasakianmanifolds. Finally, we give an example of a 3-dimensional P-Sasakian manifold.

Keywords and phrases

Para-Sasakian manifold conformal curvature tensor concircular curvature tensor cyclic parallel Ricci tensor Ricci tensor is of Codazzi type 

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References

  1. 1.
    T. Adati and K. Matsumoto, TRU Math. 13 (1), 25–32 (1977).MathSciNetGoogle Scholar
  2. 2.
    T. Adati and T. Miyazawa, TRU Math. 13 (1), 33–42 (1977).MathSciNetGoogle Scholar
  3. 3.
    D. E. Blair, J. S. Kim, and M. M. Tripathi, J. KoreanMath. Soc. 42 (5), 883–892 (2005).MathSciNetGoogle Scholar
  4. 4.
    U. C. De, Publ. Math. Debrecen 49, 33–37 (1996).MathSciNetGoogle Scholar
  5. 5.
    U. C. De and J. C. Ghosh, Note Mat. 14 (2), 155–160 (1997).MathSciNetGoogle Scholar
  6. 6.
    U. C. De and N. Guha, Istanbul Univ. Fen Fak. Mat. Derg. 51, 35–39 (1992).MathSciNetGoogle Scholar
  7. 7.
    U. C. De and D. Tarafdar, Math. Balkanica (N. S.) 7 (3-4), 211–215 (1993).MathSciNetGoogle Scholar
  8. 8.
    U. C. De, C. Ozgür, K. Arslan, C. Murathan, and A. Yildiz,Mathematica Balkanica 22 (1-2), 25–36 (2008).Google Scholar
  9. 9.
    S. Desmukh and S. Ahmed, Kyungpook J. Math. 20, 112–121 (1980).Google Scholar
  10. 10.
    R. Deszcz, L. Verstraelen, and S. Yaprak, Chin. J. Math. 22 (2), 139–157 (1994).MathSciNetGoogle Scholar
  11. 11.
    A. Gray, Geom. Dedicata 7, 259–280 (1978).MathSciNetCrossRefGoogle Scholar
  12. 12.
    U-H. Ki and H. Nakagawa, Tohoku Math. J. 39, 27–40 (1987).MathSciNetGoogle Scholar
  13. 13.
    K. Matsumoto, S. Ianus, and I. Mihai, Publ. Math. Debrecen 33, 61–65 (1986).MathSciNetGoogle Scholar
  14. 14.
    C. Ozgür, Turkish J. Math. 29 (3), 249–257 (2005).MathSciNetGoogle Scholar
  15. 15.
    I. Sato, Tensor (N.S.) 30 (3), 219–224 (1976).MathSciNetGoogle Scholar
  16. 16.
    I. Sato and K. Matsumoto, Tensor, N. S. 33, 173–178 (1979).MathSciNetGoogle Scholar
  17. 17.
    P. Shirokov, Tensor Calculus, Part 1: Tensor Algebra (Gostekhteorizdat, Moscow, 1934) [in Russian].Google Scholar
  18. 18.
    Z. I. Szabó, J. Diff. Geometry 17, 531–582 (1982).Google Scholar
  19. 19.
    Y. Tashiro, Trans. Am. Math. Soc. 117, 251–275 (1965).MathSciNetCrossRefGoogle Scholar
  20. 20.
    K. Yano, Proc. Imp. Acad. Tokyo 16, 195–200 (1940).MathSciNetCrossRefGoogle Scholar
  21. 21.
    K. Yano and M. Kon, Structures on Manifolds. Series in Pure Mathematics (World Scientific, Singapore, 1984).MATHGoogle Scholar
  22. 22.
    A. Yildiz, M. Turan, and B. E. Acet, Dumlupinar üniversitesi 24, 27–34 (2011).Google Scholar

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© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of CalcuttaWest BengalIndia

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