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 language | English |
|---|---|
| Pages (from-to) | 43-58 |
| Number of pages | 16 |
| Journal | Geometriae Dedicata |
| Volume | 183 |
| Issue number | 1 |
| Early online date | 13 Feb 2016 |
| DOIs | |
| Publication status | Published - 1 Aug 2016 |
Keywords
- Isothermic surface
- Discrete isothermic net
- Calapso transformation
- Darboux transformation
- Bianchi permutability
- Lawson correspondence
- Bäcklund transformation
- Constant mean curvature
