Special isothermic surfaces of type $d$

TL;DR

This paper explores special isothermic surfaces of type d, explaining their properties through gauge theory, and extends the classification to higher codimensions, enriching the geometric theory.

Contribution

It introduces a hierarchy of special isothermic surfaces and generalizes the theory to arbitrary codimension using gauge-theoretic methods.

Findings

Special isothermic surfaces fit into a hierarchy.

The gauge-theoretic approach simplifies understanding of these surfaces.

Extension of the theory to arbitrary codimension.

Abstract

The special isothermic surfaces, discovered by Darboux in connection with deformations of quadrics, admit a simple explanation via the gauge-theoretic approach to isothermic surfaces. We find that they fit into a heirarchy of special classes of isothermic surface and extend the theory to arbitrary codimension.