A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds

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.