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arXiv · 2502.11815

A purely analytic derivation of Bonnet surfaces

Robert Conte·A. Michel Grundland
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Abstract

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 Painlev\'e property.

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Robert Conte, A. Michel Grundland. 2025-02-17. A purely analytic derivation of Bonnet surfaces. https://arxiv.org/abs/2502.11815

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