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

Authors : Dibakar Dey

Pages : 388-394

View : 21 | Download : 11

Publication Date : 2019-10-15

Article Type : Research Paper

Abstract :The object of the present paper is to characterize $\xi$-conformally flat $insert ignore into journalissuearticles values(k,\mu);$-almost Kenmotsu manifolds and $insert ignore into journalissuearticles values(k,\mu);`$-almost Kenmotsu manifolds. It is proved that a $insert ignore into journalissuearticles values(k,\mu);$-almost Kenmotsu manifold is $\xi$-conformally flat if and only if the manifold is an Einstein manifold. Further it is shown that a $insert ignore into journalissuearticles values(2n+1);$-dimensional $insert ignore into journalissuearticles values(k,\mu);`$-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