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| Certain Curvature Conditions on P-Sasakian Manifolds Admitting a Quater-Symmetric Metric Connection |
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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 |
| Page view： 1145
Net amount： 735 |
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). |
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| 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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