- Konuralp Journal of Mathematics
- Vol: 7 Issue: 2
- A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds
A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds
Authors : Dibakar Dey
Pages : 388-394
View : 9 | Download : 4
Publication Date : 2019-10-15
Article Type : Research
Abstract :The object of the present paper is to characterize $\xi$-conformally flat $(k,\mu)$-almost Kenmotsu manifolds and $(k,\mu)'$-almost Kenmotsu manifolds. It is proved that a $(k,\mu)$-almost Kenmotsu manifold is $\xi$-conformally flat if and only if the manifold is an Einstein manifold. Further it is shown that a $(2n+1)$-dimensional $(k,\mu)'$-almost Kenmotsu manifold is $\xi$-conformally flat if and only if it is conformally flat. As a consequence of the main results we obtain several corollaries. Finally, we give an example to verify our result.Keywords : Almost Kenmotsu manifold, Einstein manifold, Riemannian curvature tensor, Ricci tensor, Weyl conformal curvature tensor