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

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