Geometry of $(\kappa,\mu)'$-almost Kenmotsu manifolds with divergence free Cotton tensor and vanishing Bach tensor

In this paper, we prove that a non-Kenmotsu $(\kappa,\mu)'$-almost Kenmotsu manifold of dimension $(2n+1)$ has divergence free Cotton tensor if and only if it is locally isometric to the Riemannian product $\mathbb{H}^{n+1}(-4)\times\mathbb{R}^n$. Finally, we show that a Bach flat non-Kenmotsu $(\kappa,\mu)'$-almost Kenmotsu manifold is 3-dimensional and is locally isometric to the Riemannian product $\mathbb{H}^2(-4)\times\mathbb{R}$.