Certain almost Kenmotsu metrics satisfying the Miao—Tam equation

In this paper, we consider the Miao—Tam equation within the frame-work of Kenmotsu and almost Kenmotsu manifolds. These classes have a nice connection with the warped product of real line and almost Hermitian (Kähler) manifolds. Here, we prove that a Kenmotsu metric satisfying the Miao—Tam equation is Einstein. Next, we study the Miao—Tam equation on almost Kenmotsu manifolds satisfying some nullity conditions. To this end, we construct some examples of almost Kenmotsu manifolds that satisfy the Miao—Tam equation.