The Bianchi-Darboux transform of L-isothermic surfaces

2000/01/11 by Emilio Musso, E. Musso, Musso, E. +3
Mathematics · Physics and Astronomy · #53A05 #53A40 #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons #math.DG #msc:53A05 #msc:53A40

paper · pdf · doi:10.48550/arxiv.math/0001062

13 pages, amstex, to be published in IJM

arxiv created 2000/01/11 · openalex publication_date 2000/01/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study an analogue of the classical Bianchi-Darboux transformation for L-isothermic surfaces in Laguerre geometry, the Bianchi-Darboux transformation. We show how to construct the Bianchi-Darboux transforms of an L-isothermic surface by solving an integrable linear differential system. We then establish a permutability theorem for iterated Bianchi-Darboux transforms.

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