Semi-discrete isothermic surfaces (Q5891062)

The authors study semi-discrete surfaces in the form of maps from \(\mathbb{Z} \times \mathbb{R}\) to 3-dimensional Euclidean space, which can be interpreted as semi-discretizations of smooth surfaces (one of the parameters is made discrete). They define and develop the relevant notions of circular surfaces, isothermic surfaces, conformal mappings, and dualizability (in the sense of Christoffel). They discuss a semi-discrete version of Koenigs nets, they show that isothermicity is equivalent to dualizability for circular surfaces, and they give a characterization of isothermic surfaces.