TANGENT BUNDLES OF LP-SASAKIAN MANIFOLD ENDOWED WITH GENERALIZED SYMMETRIC METRIC CONNECTION

The aim of the present work is to study and establish conditions for anLP-Sasakian manifold on the tangent bundle $TM$. An LP-Sasakian manifold with the generalized symmetric metric connection on $TM$ is investigated. Next, the curvature tensor and the Ricci tensor of an LP-Sasakian manifold with respect to the generalized symmetric metric connection on $TM$ are calculated. Moreover, the projective curvature tensor with respect to the generalized symmetric metric connection on $TM$ is studied and showed that $TM$ is not $\hat{\xi}^C$-projectively flat. In particular, if $\alpha=0$ and $\beta=1$ then $TM$ is $\hat{\xi}^C$-projectively flat