Discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3 : a discrete Lawson correspondence

Alexander I Bobenko (1) , Pascal Romon (2)

1 Institut für Mathematik [Berlin]
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

The main result of this paper is a discrete Lawson correspondence between discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. This is a correspondence between two discrete isothermic surfaces. We show that this correspondence is an isometry in the following sense: it preserves the metric coefficients introduced previously by Bobenko and Suris for isothermic nets. Exactly as in the smooth case, this is a correspondence between nets with the same Lax matrices, and the immersion formulas also coincide with the smooth case.

Mots clés: integrable systems; discrete surfaces; integrable systems; constant mean curvature; minimal surface; discrete isometry

Domaines: Géométrie différentielle [math.DG]; Systèmes Solubles et Intégrables [nlin.SI]

Alexander I Bobenko, Pascal Romon. Discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3 : a discrete Lawson correspondence. Journal of Integrable Systems, 2017, 2 (1), pp.1-18. ⟨10.1093/integr/xyx010⟩. ⟨hal-01517411v2⟩