On Generalized Weyl Conformal Curvature Tensor in Para-Kenmotsu Manifolds
On Generalized Weyl Conformal Curvature Tensor
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Keywords:
Weyl conformal curvature tensor, para-Kenmotsu manifolds, Einstein manifold, generalized Weyl conformal curvature tensorAbstract
In the present study, we consider a generalized Weyl conformal curvature tensor on para-Kenmotsu manifolds (briefly, $PK$-manifolds). First we describe certain vanishing properties of generalized Weyl conformal curvature tensor (brifly, GWC-curvature tensor) on a $PK$-manifold. Later, we study generalized Weyl conformally semi-symmetric $PK$-manifold that turns out to an Einstein manifold. Among others, it has been shown that the generalized Weyl conformally $\phi$-symmetric $PK$-manifold is of constant curvature or $dr (\psi)=0$.
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