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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.11815 |
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| _version_ | 1866917925784387584 |
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| author | Conte, Robert Grundland, A. Michel |
| author_facet | Conte, Robert Grundland, A. Michel |
| contents | Bonnet has characterized his surfaces by a geometric condition. What is done here is a characterization of the same surfaces by two analytic conditions: (i) the mean curvature $H$ of a surface in $\mathbb{R}^3$ should admit a reduction to an ordinary differential equation; (ii) this latter equation should possess the Painlevé property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11815 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A purely analytic derivation of Bonnet surfaces Conte, Robert Grundland, A. Michel Differential Geometry Mathematical Physics 33E17, 34Mxx, 35A20, 35Q99 Bonnet has characterized his surfaces by a geometric condition. What is done here is a characterization of the same surfaces by two analytic conditions: (i) the mean curvature $H$ of a surface in $\mathbb{R}^3$ should admit a reduction to an ordinary differential equation; (ii) this latter equation should possess the Painlevé property. |
| title | A purely analytic derivation of Bonnet surfaces |
| topic | Differential Geometry Mathematical Physics 33E17, 34Mxx, 35A20, 35Q99 |
| url | https://arxiv.org/abs/2502.11815 |