Willmore surfaces in spheres: the DPW approach via the conformal Gauss map

Abstract

The paper builds a DPW approach of Willmore surfaces via conformal Gauss maps. As applications, we provide descriptions of minimal surfaces in ${\mathbb{R}}^{n+2}$, isotropic surfaces in $S^4$ and homogeneous Willmore tori via the loop group method. A new example of a Willmore two-sphere in $S^6$ without dual surfaces is also presented.

23 pages. Following the suggestion of some anonymous referee we have divided the paper entitled "Willmore surfaces in spheres via loop groups I: generic cases and some examples" (arXiv:1301.2756) into three parts. The present paper is part II and [15,16] are part I and part III respectively

References in corpus (1)

• Willmore surfaces in spheres via loop groups IV: on totally isotropic Willmore two-spheres in $S^6$