On Einstein-type almost Kenmotsu manifolds

Abstract

Abstract First, we consider a non-trivial Einstein-type equation on a Kenmotsu manifold M and show that either M is Einstein or the potential function is pointwise collinear with ξ on an open set 𝒰 {\mathcal{U}} of M. Finally, we study an Einstein-type equation on an almost Kenmotsu ( κ , μ ) ′ {(\kappa,\mu)^{\prime}} -manifold.