Certain Curvature Conditions on P-Sasakian Manifolds Admitting a Quater-Symmetric Metric Connection
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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 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 semisymmetric2000 MR Subject Classification
53C35 53D40Preview
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Acknowledgement
The fourth author would like to thank Professor P. B. Zhao and U. C. De for their help.
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