# On conformal Gauss maps

## TL;DR

This paper characterizes conformal Gauss maps of surfaces in spheres, providing an invariant formulation and a streamlined proof of their relation to harmonic maps of Willmore surfaces.

## Contribution

It offers a new invariant approach and an efficient proof for identifying conformal Gauss maps of Willmore surfaces, extending prior characterizations.

## Key findings

- Invariant formulation of conformal Gauss maps
- Characterization of harmonic maps as conformal Gauss maps
- Simplified proof of the Dorfmeister--Wang result

## 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.