Willmore Surfaces in Spheres via Loop Groups Ⅳ:On Totally Isotropic Willmore Two-Spheres in S6

• 作者: Peng WANG
• 来源期刊: 数学年刊B辑（英文版）
• 年，卷（期）: 2021,（3）
• 页码范围: 383-408
• 页数: 26页
• 语种: 英文
• DOI: 10.1007/s11401-021-0265-6

摘要

In this paper the author derives a geometric characterization of totally isotropic Willmore two-spheres in S6,which also yields to a description of such surfaces in terms of the loop group language.Moreover,applying the loop group method,he also obtains an algorithm to construct totally isotropic Willmore two-spheres in S6.This allows him to derive new examples of geometric interests.He first obtains a new,totally isotropic Willmore two-sphere which is not S-Willmore(i.e.,has no dual surface)in S6.This gives a negative answer to an open problem of Ejiri in 1988.In this way he also derives many new totally isotropic,branched Willmore two-spheres which are not S-Willmore in S6.