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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