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- Title
Willmore surfaces of constant Möbius curvature.
- Authors
Xiang Ma; Changping Wang
- Abstract
Abstract  We study Willmore surfaces of constant M�bius curvature $${\mathcal{K}}$$ in $${\mathbb{S}}^4$$ . It is proved that such a surface in $${\mathbb{S}}^3$$ must be part of a minimal surface in $${\mathbb{R}}^3$$ or the Clifford torus. Another result in this paper is that an isotropic surface (hence also Willmore) in $${\mathbb{S}}^4$$ of constant $${\mathcal{K}}$$ could only be part of a complex curve in $${\mathbb{C}}^2 \cong {\mathbb{R}}^4$$ or the Veronese 2-sphere in $${\mathbb{S}}^4$$ . It is conjectured that they are the only possible examples. The main ingredients of the proofs are over-determined systems and isoparametric functions.
- Subjects
MAXIMA &; minima; MINIMAL surfaces; GAUSS maps; CURVES
- Publication
Annals of Global Analysis & Geometry, 2007, Vol 32, Issue 3, p297
- ISSN
0232-704X
- Publication type
Article
- DOI
10.1007/s10455-007-9065-9