The topology of 3-dimensional Hessian manifolds

2025/10/23 by Gnandi, Emmanuel
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.21050

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.

Citations

• An Introduction to Geometric Topology
• A universal model for cosymplectic manifolds

Related

• On Topology of Compact Hessian Manifolds
• Higher order Hessian structures on manifolds
• Selfsimilar Hessian and conformally Kähler manifolds
• Selfsimilar Hessian manifolds
• Hessian geometry on Lagrange spaces