Willmore surfaces in spheres via loop groups. III: On minimal surfaces in space forms. (English) Zbl 1368.53010

This article under review is the third paper of a series of papers concerning the global geometry of Willmore surfaces in terms of loop group theory. In the first part of the paper, the forms of the normalized potentials of strongly conformally harmonic maps containing a non-zero constant real vector is derived. In the last part of the paper, expressing the normalized potentials by some strictly upper triangular matrix-valued 1-forms, the author gives by direct computations a concrete description of all Willmore surfaces corresponding to the first type of nilpotent Lie subalgebras investigated in the second article of the series [the author, “Willmore surfaces in spheres via loop groups. II: A coarse classification of Willmore two-spheres by potentials”, Preprint, arxiv:1412.6737].
For Part IV, see [the author, Chin. Ann. Math., Ser. B 42, No. 3, 383–408 (2021; Zbl 1473.53086)].


53A30 Conformal differential geometry (MSC2010)
58E20 Harmonic maps, etc.
53C43 Differential geometric aspects of harmonic maps
53C35 Differential geometry of symmetric spaces


Zbl 1473.53086
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