The conformal Gauss map of submanifolds of the Möbius space

DOI10.1007/BF00127853zbMath0642.53014WikidataQ125659193 ScholiaQ125659193MaRDI QIDQ1101691

Marco Rigoli

Publication date: 1987

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

zbMATH Keywords

Willmore functionalWillmore surfaceumbilical pointsconformal Gauss mapMöbius spaceconformal total curvature

Mathematics Subject Classification ID

Global submanifolds (53C40)

Related Items (15)

Quartic differentials and harmonic maps in conformal surface geometry ⋮ Simple factor dressing and the López-Ros deformation of minimal surfaces in Euclidean 3-space ⋮ The \(\mu\)-Darboux transformation of minimal surfaces ⋮ On conformal Gauss maps ⋮ Variational problems of normal curvature tensor and concircular scalar fields. ⋮ Willmore surfaces in the four-sphere ⋮ Unnamed Item ⋮ Applications of quaternionic holomorphic geometry to minimal surfaces ⋮ WEIERSTRASS–KENMOTSU REPRESENTATION OF WILLMORE SURFACES IN SPHERES ⋮ Spectral deformation and Bäcklund transformation of constrained Willmore surfaces ⋮ Minimal surfaces under constrained Willmore transformation ⋮ Willmore surfaces in spheres: the DPW approach via the conformal Gauss map ⋮ On Willmore surfaces in 𝑆ⁿ of flat normal bundle ⋮ Möbius isotropic submanifolds in \(\mathbb{S}^n\) ⋮ Willmore submanifolds of the Möbius space and a Bernstein-type theorem

Cites Work

• Unnamed Item
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• A duality theorem for Willmore surfaces
• On the volume of the generalized Gauss map
• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• The Gauss map of immersions of Riemannian manifolds in spaces of constant curvature
• Submanifolds of the Möbius space
• Conformal Differential Geometry of a Subspace

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