On Two Dimensional Flat Hessian Potentials

Fuente: arXiv
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Main Author: Liu, Hanwen
Format: Preprint
Published: 2025
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author Liu, Hanwen
author_facet Liu, Hanwen
contents 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 function. Under very mild extra technical conditions, we first theoretically describe the potentials of flat Hessian metrics on surfaces, and then construct these potentials explicitly using methods from integrable systems.
format Preprint
id arxiv_https___arxiv_org_abs_2512_15079
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On Two Dimensional Flat Hessian Potentials
Liu, Hanwen
Differential Geometry
Mathematical Physics
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 function. Under very mild extra technical conditions, we first theoretically describe the potentials of flat Hessian metrics on surfaces, and then construct these potentials explicitly using methods from integrable systems.
title On Two Dimensional Flat Hessian Potentials
topic Differential Geometry
Mathematical Physics
url https://arxiv.org/abs/2512.15079