Classification of Quasi-Einstein Structure on Three-Dimensional Homogeneous Almost \(\alpha \)-Cosympletic Manifolds

The purpose of the paper is to categorize quasi-Einstein structures on simply connected three-dimensional homogeneous almost \(\alpha \) $\alpha$ -cosympletic manifolds, where the Reeb vector field is an eigenvector of the Ricci operator. This is achieved by assuming that the potential vector field of the quasi-Einstein structure is both pointwise collinear and transversal to the Reeb vector field at every point. The paper concludes by constructing an instance of a hyperbolic space, denoted as \({\mathbb {H}}^3(-\alpha ^2)\) ${\mathbb{H}}^3(-{\alpha }^2)$ , which satisfies the quasi-Einstein structure.