Almost Kenmotsu Manifolds Admitting Certain Critical Metric
Abstract
In the present paper, we introduce the notion of -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,μ)'-almost Kenmotsu manifold (M,g) satisfies the -Miao-Tam critical equation, then the manifold (M,g) is -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.
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