The topology of 3-dimensional Hessian manifolds

Abstract: This paper investigates the global topology of three-dimensional Hessian manifolds. We prove that every compact, orientable Hessian 3-manifold is either the Hantzsche Wendt manifold or admits the structure of a Kahler mapping torus. This result highlights a deep and intrinsic relationship between Hessian and Kahler geometries. Furthermore, we provide a classification of compact, orientable, three-dimensional Hessian manifolds.