A purely analytic derivation of Bonnet surfaces

Obtention purement analytique des surfaces de Bonnet

R. Conte (1) , A. Michel Grundland (2, 3)

1 CB - CB - Centre Borelli - UMR 9010
2 CRM - Centre de Recherches Mathématiques [Montréal]
3 UQTR - Université du Québec à Trois-Rivières

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.

Mots clés: Bonnet surfaces; Gauss-Codazzi equations; sixth equation of Painlevé

Domaines: Science non linéaire [physics]; Science non linéaire [physics]

R. Conte, A. Michel Grundland. A purely analytic derivation of Bonnet surfaces. Journal of Geometry and Physics, 2025, 211, pp.105454. ⟨10.1016/j.geomphys.2025.105454⟩. ⟨hal-04951980⟩