On conformal Gauss maps

Abstract

We characterise the maps into the space of $2$-spheres in $S^n$ that are the conformal Gauss maps of conformal immersions of a surface. In particular, we give an invariant formulation and efficient proof of a characterisation, due to Dorfmeister--Wang \cites{DorWan13,DorWan}, of the harmonic maps that are conformal Gauss maps of Willmore surfaces.

5 pages. v2: minor corrections

References in corpus (1)

• Willmore surfaces in spheres via loop groups $I$: generic cases and some examples