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

Peng Wang

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arXiv · 1412.8135

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

Peng Wang

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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.

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BibTeX RIS

Peng Wang. 2014-12-28. Willmore surfaces in spheres via loop groups IV: on totally isotropic Willmore two-spheres in $S^6$. https://arxiv.org/abs/1412.8135

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