Almost Kenmotsu Manifolds Admitting Certain Critical Metric

Abstract

Abstract The object of this offering article is to introduce the notion of *- Miao-Tam critical equation on almost contact metric manifolds and it is studied on almost Kenmotsu manifolds with some nullity condition. It is proved 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 a product space. Finally, the result is verified by an example.