# A complex associated family for isothermic surfaces

## University of Leicester

In my talk I explain how Quaternionic Holomorphic Geometry can be used to discuss the associated family of isothermic surfaces. Isothermic surfaces are surfaces which have a conformal curvature line parametrisation, and cylinder, minimal surfaces and constant mean curvature surfaces are examples. It is known that any isothermic surface has a family of flat real connections such that parallel sections give new isothermic surfaces. In this talk, I will introduce a complex family which specialises to the known complex families for minimal surfaces and constant mean curvature surfaces.