Transformations of discrete isothermic nets and discrete cmc-1 surfaces in hyperbolic space

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• 作者：Udo Hertrich-Jeromin
• 刊名：manuscripta mathematica
• 出版年：2000
• 出版时间：August 2000
• 年：2000
• 卷：102
• 期：4
• 页码：465-486
• 全文大小：398 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebraic Geometry
  Topological Groups and Lie Groups
  Geometry
  Number Theory
  Calculus of Variations and Optimal Control
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1785

文摘

Using a quaternionic calculus, the Christoffel, Darboux, Goursat, and spectral transformations for discrete isothermic nets are described, with their interrelations. The Darboux and spectral transformations are used to define discrete analogs for cmc-1 surfaces in hyperbolic space and to obtain a discrete version of Bryant's Weierstrass type representation.