Semi-discrete isothermic surfaces

被引：11
|
作者：
Burstall, F. [1 ]
Hertrich-Jeromin, U. [2 ]
Mueller, C. [2 ]
Rossman, W. [3 ]
机构：
[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England
[2] Vienna Univ Technol, Wiedner Hauptstr 8-10-104, A-1040 Vienna, Austria
[3] Kobe Univ, Dept Math, Kobe, Hyogo 6578501, Japan
来源：
GEOMETRIAE DEDICATA | 2016年 / 183卷 / 01期
基金：
奥地利科学基金会; 日本学术振兴会;
关键词：
Isothermic surface; Discrete isothermic net; Calapso transformation; Darboux transformation; Bianchi permutability; Lawson correspondence; Backlund transformation; Constant mean curvature;
D O I：
10.1007/s10711-016-0143-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A Darboux transformation for polarized space curves is introduced and its properties are studied, in particular, Bianchi permutability. Semi-discrete isothermic surfaces are described as sequences of Darboux transforms of polarized curves in the conformal n-sphere and their transformation theory is studied. Semi-discrete surfaces of constant mean curvature are studied as an application of the transformation theory.
引用
收藏
页码：43 / 58
页数：16
相关论文
共 50 条
  • [1] Semi-discrete isothermic surfaces
    F. Burstall
    U. Hertrich-Jeromin
    C. Müller
    W. Rossman
    Geometriae Dedicata, 2016, 183 : 43 - 58
  • [2] Semi-Discrete Isothermic Surfaces
    Christian Müller
    Johannes Wallner
    Results in Mathematics, 2013, 63 : 1395 - 1407
  • [3] Semi-Discrete Isothermic Surfaces
    Mueller, Christian
    Wallner, Johannes
    RESULTS IN MATHEMATICS, 2013, 63 (3-4) : 1395 - 1407
  • [4] A Laplace Operator on Semi-Discrete Surfaces
    Wolfgang Carl
    Foundations of Computational Mathematics, 2016, 16 : 1115 - 1150
  • [5] A Laplace Operator on Semi-Discrete Surfaces
    Carl, Wolfgang
    FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2016, 16 (05) : 1115 - 1150
  • [6] Semi-discrete constant mean curvature surfaces
    Christian Müller
    Mathematische Zeitschrift, 2015, 279 : 459 - 478
  • [7] Semi-discrete constant mean curvature surfaces
    Mueller, Christian
    MATHEMATISCHE ZEITSCHRIFT, 2015, 279 (1-2) : 459 - 478
  • [8] Discrete isothermic surfaces
    Bobenko, A
    Pinkall, U
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1996, 475 : 187 - 208
  • [9] Discrete special isothermic surfaces
    Burstall, F.
    Hertrich-Jeromin, U.
    Rossman, W.
    Santos, S.
    GEOMETRIAE DEDICATA, 2015, 174 (01) : 1 - 11
  • [10] Discrete special isothermic surfaces
    F. Burstall
    U. Hertrich-Jeromin
    W. Rossman
    S. Santos
    Geometriae Dedicata, 2015, 174 : 1 - 11
12345