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

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Abstract

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.

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Acknowledgement

The author is thankful to Professor Josef Dorfmeister, Professor Changping Wang and Professor Xiang Ma for their suggestions and encouragement.

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Authors and Affiliations

  1. College of Mathematics & Informatics, FJKLMAA, Fujian Normal University, Qishan Campus, Fuzhou, 350117, China

    Peng Wang

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  1. Peng Wang
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Correspondence to Peng Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11971107, 11571255).

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Wang, P. Willmore Surfaces in Spheres via Loop Groups IV: On Totally Isotropic Willmore Two-Spheres in S6. Chin. Ann. Math. Ser. B 42, 383–408 (2021). https://doi.org/10.1007/s11401-021-0265-6

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  • DOI: https://doi.org/10.1007/s11401-021-0265-6

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