Quaternionic analysis on Riemann surfaces and differential geometry

zbMath0910.53042MaRDI QIDQ1126787

Franz J. Pedit, Ulrich Pinkall

Publication date: 6 August 1998

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/231230

zbMATH Keywords

Willmore functionalquaternionic analysisconformal mapsCauchy-Riemann equationsholomorphic line bundlesconformal immersionquaternionic line bundlessurfaces in \(\mathbb R^4\)

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Holomorphic bundles and generalizations (32L05)

Related Items (17)

Twistor lifts and factorization for conformal maps from a surface to the Euclidean four-space ⋮ Generalized Weierstrass representation of surfaces in \(\mathbb R^4\) ⋮ Isothermic triangulated surfaces ⋮ A condition for a closed one-form to be exact ⋮ Surfaces via spinors and soliton equations ⋮ The periodic N breather anomalous wave solution of the Davey–Stewartson equations; first appearance, recurrence, and blow up properties ⋮ The denominators of Lagrangian surfaces in complex Euclidean plane ⋮ Generalized Weierstrass relations and Frobenius reciprocity ⋮ Applications of quaternionic holomorphic geometry to minimal surfaces ⋮ Infinitesimal conformal deformations of triangulated surfaces in space ⋮ The quaternionic KP hierarchy and conformally immersed 2-tori in the 4-sphere ⋮ The spacelike surface with parallel mean curvature vector in \(\mathbb R^{3, 1}\) ⋮ Soliton spheres ⋮ Finding conformal and isometric immersions of surfaces ⋮ The spectral curve of a quaternionic holomorphic line bundle over a 2-torus ⋮ Polar varieties and bipolar surfaces of minimal surfaces in the \(n\)-sphere ⋮ A factorization of a super-conformal map

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