Abstract The goal of this article is to find some geometric characterizations of Kenmotsu and almost Kenmotsu manifolds that admit a non-gradient m -quasi-Einstein structure. First, we prove that a Kenmotsu manifold admits a closed m -quasi-Einstein structure is an Einstein manifold. Next, we prove that if a three-dimensional Kenmotsu manifold admits a non-trivial m -quasi-Einstein structure (g, V, m, ) with V as a conformal vector field, then it is of constant sectional curvature -1. Finally, we prove that if a non-Kenmotsu almost Kenmotsu (k, ) ^ -manifold admits a closed m -quasi-Einstein structure (g, V, m, ) with m 1, then it is locally isometric to the product space H^n+1 (-4) R^n.
Dhriti Sundar Patra (Mon,) studied this question.