Constant mean curvature tori with spherical curvature lines in noneuclidean geometry

DOI10.1007/BF01168376zbMath0679.53006MaRDI QIDQ1822770

Rolf Walter

Publication date: 1989

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

Full work available at URL: https://eudml.org/doc/155386

zbMATH Keywords

hyperbolic spaceconstant mean curvaturestandard sphereTori

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) Non-Euclidean differential geometry (53A35)

Related Items (6)

Classical dynamics of the rigid string from the Willmore functional ⋮ On the role of the Burstin-Mayer metric for surfaces in \(\mathbb{R}^ 4\) ⋮ Free boundary minimal annuli immersed in the unit ball ⋮ Non-special, non-canal isothermic tori with spherical lines of curvature ⋮ All constant mean curvature tori in \(R^ 3\), \(S^ 3\), \(H^ 3\) in terms of theta-functions ⋮ Discrete Conformal Maps: Boundary Value Problems, Circle Domains, Fuchsian and Schottky Uniformization

Cites Work

• Unnamed Item
• Compact hypersurfaces with a constant higher mean curvature function
• Counterexample to a conjecture of H. Hopf
• Complete minimal surfaces in \(S^ 3\)
• Constant mean curvature tori in terms of elliptic functions.
• Explicit examples to the H-problem of Heinz Hopf

This page was built for publication: Constant mean curvature tori with spherical curvature lines in noneuclidean geometry