On the $m$-quasi-Einstein almost contact manifolds

In this paper, we consider the $m$-quasi Einstein metric on certain classes of almost Kenmotsu manifolds. First, we prove that if a Kenmotsu manifold admits $m$-quasi Einstein metric, then it is either trivial (Einstein) or locally isometric to a warped product space. We also provide an example of $m$-quasi-Einstein Kenmotsu metric. Finally, we prove that a non-Kenmotsu $(\kappa,\mu)'$-almost Kenmotsu manifold admitting an $m$-quasi-Einstein metric is locally isometric to the Riemannian product $\mathbb{H}^{n+1}(-4)\times\mathbb{R}^{n}$.