Semi-discrete isothermic surfaces

Francis Burstall, Udo Hertrich-Jeromin, Christian Müller, Wayne Rossman

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5 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)43-58
Number of pages16
JournalGeometriae Dedicata
Volume183
Issue number1
Early online date13 Feb 2016
DOIs
Publication statusPublished - 1 Aug 2016

Keywords

  • Isothermic surface
  • Discrete isothermic net
  • Calapso transformation
  • Darboux transformation
  • Bianchi permutability
  • Lawson correspondence
  • Bäcklund transformation
  • Constant mean curvature

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Cite this

Burstall, F., Hertrich-Jeromin, U., Müller, C., & Rossman, W. (2016). Semi-discrete isothermic surfaces. Geometriae Dedicata, 183(1), 43-58. https://doi.org/10.1007/s10711-016-0143-7