Semi-discrete isothermic surfaces
arXiv:1506.04730 · doi:10.1007/s10711-016-0143-7
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.
plain TeX, 12 pages
References in corpus (7)
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- Discrete linear Weingarten surfaces
- Special isothermic surfaces of type
- Orthogonal nets and Clifford algebras
- Discrete surfaces of constant mean curvature
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Cited by in corpus (7)
- Channel surfaces in Lie sphere geometry
- Ribaucour coordinates
- Periodic discrete Darboux transforms
- Discrete mKdV equation via Darboux transformation
- Infinitesimal Darboux transformation and semi-discrete mKdV equation
- Constructing solutions to the Björling problem for isothermic surfaces by structure preserving discretization
- Isothermic surfaces and conservation laws