Classification of Quasi-Einstein Structure on Three-Dimensional Homogeneous Almost α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-Cosympletic Manifolds

The purpose of the paper is to categorize quasi-Einstein structures on simply connected three-dimensional homogeneous almost α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-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 H3(-α2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {H}}^3(-\alpha ^2)$$\end{document}, which satisfies the quasi-Einstein structure.