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math.DG2025
On Two Dimensional Flat Hessian Potentials
Hanwen Liu
A Riemannian metric is termed a Hessian metric if in some coordinate system it can be locally represented as the Hessian quadratic form of some locally defined smooth potential fun…
math.DG2025
On Topology of Compact Hessian Manifolds
Hanwen Liu
We investigate the global topological constraints and structural properties of compact Hessian manifolds. By establishing novel fibration and splitting theorems, we confirm Chern's…