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

Abstract

Totally isotropic surfaces in $S^6$ are not necessarily Willmore surfaces. Therefore it is the first goal of this paper to derive a geometric characterization of totally isotropic Willmore two-spheres in $S^6$. This will naturally yield to a description of such surfaces in terms of the loop group language. Moreover, applying the loop group method, we also obtain an algorithm to construct totally isotropic Willmore two-spheres in $S^6$. As an application, a new, totally isotropic Willmore two-sphere which is not S-Willmore (i.e., has no dual surface) in $S^6$ is constructed, illustrating the theory of this paper.

26 pages, adding more explanations for the computations

References in corpus (1)

• Classification of Willmore 2-spheres in the 5-dimensional sphere

Cited by in corpus (1)

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