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Chinese Annals of Mathematics, Series B

, Volume 41, Issue 1, pp 133–146 | Cite as

Certain Curvature Conditions on P-Sasakian Manifolds Admitting a Quater-Symmetric Metric Connection

  • Uday Chand De
  • Peibiao Zhao
  • Krishanu Mandal
  • Yanling HanEmail author
Article
  • 11 Downloads

Abstract

The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ricci semisymmetric P-Sasakian manifold with respect to the quarter-symmetric metric connection is considered. Next the authors study ξ-concircularly flat P-Sasakian manifolds and concircularly semisymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection. Furthermore, the authors study P-Sasakian manifolds satisfying the condition \(\tilde Z(\xi ,Y) \cdot \tilde S = 0\), where \(\tilde Z, \tilde S\) are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection. Finally, an example of a 5-dimensional P-Sasakian manifold admitting quarter-symmetric metric connection is constructed.

Keywords

Quarter-symmetric metric connection P-Sasakian manifold Ricci semi-symmetric manifold ξ-Concircularly flat Concircularly semisymmetric 

2000 MR Subject Classification

53C35 53D40 

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Notes

Acknowledgement

The fourth author would like to thank Professor P. B. Zhao and U. C. De for their help.

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Copyright information

© The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2020

Authors and Affiliations

  • Uday Chand De
    • 1
  • Peibiao Zhao
    • 2
  • Krishanu Mandal
    • 1
  • Yanling Han
    • 3
    Email author
  1. 1.Department of Pure MathematicsUniversity of CalcuttaCalcuttaIndia
  2. 2.Department of MathematicsNanjing University of Science and TechnologyNanjingChina
  3. 3.School of Mathematics and StatisticsQilu University of Technology (Shandong Academy of Sciences)JinanChina

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