Critical point equation on a class of almost Kenmotsu manifolds

In the present paper, we characterize ( k , μ ) ′ -almost Kenmotsu manifolds admitting ∗ -critical point equation. It is shown that if ( g , λ ) is a non-constant solution of the ∗ -critical point equation of a connected non-compact ( k , μ ) ′ -almost Kenmotsu manifold, then (1) the manifold M is locally isometric to H n + 1 ( - 4 ) × R n , (2) the manifold M is ∗ -Ricci flat and (3) the function λ is harmonic. Finally an illustrative example is presented.