Isothermic surfaces obtained from harmonic maps in S6

The harmonicity of a smooth map from a Riemann surface into the 6-dimensional sphere S amounts to the closeness of a certain 1-form that can be written in terms of the nearly Kähler structure of S. We will prove that the immersions F in R obtained from superconformal harmonic maps in S ⊂ S by integration of the corresponding closed 1-forms are isothermic. The isothermic surfaces so obtained include a certain class of constant mean curvature surfaces in R that can be deformed isometrically through isothermic surfaces into non-spherical pseudo-umbilical surfaces in R.