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

Citation:

Uday Chand DE,Peibiao ZHAO,Krishanu MANDAL,Yanling HAN.Certain Curvature Conditions on P-Sasakian Manifolds Admitting a Quater-Symmetric Metric Connection[J].Chinese Annals of Mathematics B,2020,41(1):133~146
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Authors:

Uday Chand DE; Peibiao ZHAO;Krishanu MANDAL;Yanling HAN

Foundation:

This work was supported by the National Natural Science Foundation of China (Nos.11871275, 11371194).
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 $\xi$-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 $\wt{Z}(\xi,Y)\cdot\wt{S}=0$, where $\wt{Z},\;\wt{S}$ 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, Riccisemi-symmetric manifold, $xi$-Concircularly flat, Concircularlysemisymmetric

Classification:

53C35, 53D40
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