Almost Kenmotsu Manifolds Admitting Certain Critical Metric

Abstract

In the present paper, we introduce the notion of $\ast$-Miao-Tam critical equation on almost contact metric manifolds and studied on a class of almost Kenmotsu manifold. It is shown that if the metric of a $(2n+1)$-dimensional $(k,\mu {)}^{\prime }$-almost Kenmotsu manifold $(M,g)$ satisfies the $\ast$-Miao-Tam critical equation, then the manifold $(M,g)$ is $\ast$-Ricci flat and locally isometric to the Riemannian product of a $(n+1)$-dimensional manifold of constant sectional curvature $-4$ and a flat $n$-dimensional manifold. Finally, an illustrative example is presented to support the main theorem.

10 pages