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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.06998 |
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Table of Contents:
- A symmetric quadratic form $g$ on a surface~$M$ is said to be locally Hessianizable if each $p\in M$ has an open neighborhood~$U$ on which there exists a local coordinate chart $(x^1,x^2):U\to\mathbb{R}^2$ and a function $f:U\to\mathbb{R}$ such that, on $U$, we have $$ g = \frac{\partial^2 f}{\partial x^i\partial x^j}\,\mathrm{d} x^i\circ\mathrm{d} x^j. $$ In this article, I show that, when $g$ is nondegenerate and smooth, it is always smoothly locally Hessianizable.