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| Willmore Surfaces in Spheres via Loop Groups IV: On Totally Isotropic Willmore Two-Spheres in S6* |
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Citation： |
Peng WANG.Willmore Surfaces in Spheres via Loop Groups IV: On Totally Isotropic Willmore Two-Spheres in S6*[J].Chinese Annals of Mathematics B,2021,42(3):383~408 |
| Page view： 555
Net amount： 348 |
Authors： |
Peng WANG; |
Foundation： |
National Natural Science Foundation of China (Nos. 11971107,11571255). |
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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. |
Keywords： |
Totally isotropic Willmore two-spheres, Normalized potential, Iwasawa decompositions |
Classification： |
53A30, 58E20, 53C43, 53C35 |
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