Concircular curvature tensor of Kenmotsu manifolds admitting generalized Tanaka-Webster connection

Abstract

The objective of the present paper is to study concircular curvature tensor of Kenmotsu manifold with respect to generalized Tanaka-Webster connection, whose concircular curvature tensor satisifies certain conditions and it is shown that if the curvature tensor of a Kenmotsu manifold admitting generalized Tanaka-Webster connection $\nabla^{*}$ vanishes, then the Kenmotsu manifold is locally isometric to the hyperbolic space $H^{2n+1}(-1)$. Further we have studied $\xi$-concircularly flat, $\phi$-concircularly flat, pseudo-concircularly flat, $C^{*} . \phi =0$, $C^{*}.S^{*}=0$ and we have shown that $R^{*} . C^{*}=R^{*} . R^{*}$. Finally, an example of a $5$-dimensional Kenmotsu manifold with respect to the generalized Tanaka-Webster connection is given to verify our result.