A purely analytic derivation of Bonnet surfaces
Obtention purement analytique des surfaces de Bonnet
Résumé
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 R^3 should admit a reduction to an ordinary differential equation; (ii) this latter equation should possess the Painlevé property.
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