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- W3098045500 abstract "We study Willmore surfaces of constant Möbius 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." @default.
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- W3098045500 date "2007-04-28" @default.
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- W3098045500 title "Willmore surfaces of constant Möbius curvature" @default.
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- W3098045500 doi "https://doi.org/10.1007/s10455-007-9065-9" @default.
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