Bonnet surfaces and isothermic surfaces

DOI10.1007/BF03322150zbMath0873.53035MaRDI QIDQ678725

Haizhong Li, Weihuan Chen

Publication date: 20 October 1997

Published in: Results in Mathematics (Search for Journal in Brave)

zbMATH Keywords

constant curvature4-manifoldssurfacesparallel mean curvatureumbilic points\(G\)-lines

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Related Items (8)

Bonnet surfaces with constant curvature ⋮ Reductions of Gauss-Codazzi Equations ⋮ Generalized Bonnet surfaces and Lax pairs of PVI ⋮ Timelike Bonnet surfaces in Lorentzian space forms. ⋮ Constructing isothermal curvature line coordinates on surfaces which admit them ⋮ Lagrangian Bonnet Problems in complex space forms ⋮ The Bonnet problem for harmonic maps to the three-sphere ⋮ Global results on Bonnet surfaces

Cites Work

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• Isometric deformation of surfaces in \(R^ 3\) preserving the mean curvature function
• Isometric deformation on surfaces in the hyperbolic 3-manifold preserving the mean curvature
• Complete minimal surfaces in \(S^ 3\)
• A Characterization of Compact Surfaces with Constant Mean Curvature
• A characterization of tori with constant mean curvature in space form
• Principal-curvature-preserving isometries of surfaces in ordinary space
• An Intrinsic Characterization of H -Deformable Surfaces

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