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

Year 2019, Volume: 7 Issue: 2, 388 - 394, 15.10.2019

Dibakar Dey

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

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