On Willmore surfaces in 𝑆ⁿ of flat normal bundle

DOI10.1090/S0002-9939-2013-11683-7zbMath1276.53011arXiv1301.2770OpenAlexW2908015555MaRDI QIDQ2845472

Peng Wang

Publication date: 30 August 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.2770

zbMATH Keywords

Clifford torusWillmore surfacesflat normal bundleWillmore sphereS-Willmore surfaces

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Cites Work

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• S\({}^ 1\)-equivariant minimal tori in \(S^ 4\) and \(S^ 1\)-equivariant Willmore tori in \(S^ 3\)
• A duality theorem for Willmore surfaces
• Willmore surfaces in the four-sphere
• Hopf tori in \(S^ 3\)
• The conformal Gauss map of submanifolds of the Möbius space
• Moebius geometry of submanifolds in \(\mathbb{S}^n\)
• Elasticae with constant slant in the complex projective plane and new examples of Willmore tori in five spheres
• Willmore tori in the 4-sphere with nontrivial normal bundle
• Willmore immersions and loop groups
• New examples of Willmore surfaces in \(S^n\)
• Willmore surfaces of constant Möbius curvature
• Generalized polar transforms of spacelike isothermic surfaces
• Adjoint transform of Willmore surfaces in \(\mathbb {S}^n\)
• Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms
• Weierstrass type representation of Willmore surfaces in \(S^n\)
• Homogeneous Minimal Surfaces in Euclidean Spheres with Flat Normal Connections
• Willmore Surfaces with a Duality in S ^N (1)
• Willmore two-spheres in the four-sphere
• Willmore tori in a wide family of conformal structures on odd dimensional spheres
• Conformal geometry of surfaces in \(S^4\) and quaternions

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