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CLASSIFICATION OF HOMOGENEOUS WILLMORE SURFACES IN S^n

Dorfmeister, Josef 大阪大学 DOI:10.18910/77231

2020.10

概要

In this note we consider homogeneous Willmore surfaces in S^<n+2>. The main result is that a homogeneous Willmore two-sphere is conformally equivalent to a homogeneous minimal twosphere in S^<n+2>, i.e., either a round two-sphere or one of the Borůvka-Veronese 2-spheres in S^<2m>. This entails a classification of all Willmore CP^1 in S^<2m>. As a second main result we show that there exists no homogeneous Willmore upper-half plane in S^<n+2> and we give, in terms of special constant potentials, a simple loop group characterization of all homogeneous surfaces which have an abelian transitive group.

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