Spectral transformation of constant mean curvature surfaces in \(\mathbb{H}^3\) and Weierstrass representation

DOI10.1007/BF02879990zbMath1100.53007OpenAlexW1896874454MaRDI QIDQ2503823

Qing Chen, Yi. Cheng

Publication date: 22 September 2006

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02879990

zbMATH Keywords

integrable systemshyperbolic spacemean curvaturespectral transformation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Soliton equations (35Q51) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (1)

The spacelike surface with parallel mean curvature vector in \(\mathbb R^{3, 1}\)

Cites Work

• Counterexample to a conjecture of H. Hopf
• Weierstrass type representation of harmonic maps into symmetric spaces
• Willmore tori with umbilic lines and minimal surfaces in hyperbolic space
• Complete surfaces of constant mean curvature-1 in the hyperbolic 3-space
• On the classification of constant mean curvature tori
• Complete minimal surfaces in \(S^ 3\)
• A parametrization of the Weierstrass formulae and perturbation of complete minimal surfaces in R3 into the hyperbolic 3-space.
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