Minimal Darboux transformations
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- 作者：Udo Hertrich-Jeromin ; Atsufumi Honda
- 关键词：Minimal surface ; Darboux transformation ; Christoffel transformation ; Goursat transformation ; Bianchi permutability ; Riccati equation ; Flat front ; Curved flat ; Hyperbolic geometry
- 刊名：Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：58
- 期：1
- 页码：81-91
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Algebra; Geometry; Algebraic Geometry; Convex and Discrete Geometry;
- 出版者：Springer Berlin Heidelberg
- ISSN：2191-0383
- 卷排序：58
文摘
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.