Minimal Darboux transformations

2016/02/22 by Udo Hertrich-Jeromin, Hertrich-Jeromin, U., Atsufumi Honda +1
Materials Science · Mathematics · #34M45 (Secondary) #37K25 #37K35 (Primary) #53A10 #53A30 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #Point processes and geometric inequalities #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.1602.06682

openalex publication_date 2016/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a permutability theorem for the Christoffel, Goursat and Darboux transformations of isothermic surfaces. As a consequence we obtain a simple proof of a relation between Darboux pairs of minimal surfaces in Euclidean space, curved flats in the 2-sphere and flat fronts in hyperbolic space.

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