TANGENT BUNDLES OF LP-SASAKIAN MANIFOLD ENDOWED WITH GENERALIZED SYMMETRIC METRIC CONNECTION
Abstract
The aim of the present work is to study and establish conditions for an
LP-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.
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DOI: https://doi.org/10.22190/FUMI221026009K
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