Non-special, non-canal isothermic tori with spherical lines of curvature

DOI10.1090/S0002-9947-00-02691-XzbMath0995.53006MaRDI QIDQ2706611

Holly Bernstein

Publication date: 20 March 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

conformal geometryDarboux transformationisothermic surfacechannel surfaceJFM 55.0422.01Calapso equationCalapso potentialJFM 30.0555.02JFM 36.0674.01pentaspherical coordinatesspherical curvature line

Mathematics Subject Classification ID

Related Items (8)

Deformation and applicability of surfaces in Lie sphere geometry ⋮ Infinitesimal Darboux transformation and semi-discrete MKDV equation ⋮ Constrained elastic curves and surfaces with spherical curvature lines ⋮ Darboux transforms and spectral curves of constant mean curvature surfaces revisited ⋮ Marginally outer trapped surfaces in de Sitter space by low-dimensional geometries ⋮ Channel surfaces in Lie sphere geometry ⋮ Discrete special isothermic surfaces ⋮ Darboux transforms and spectral curves of Hamiltonian stationary Lagrangian tori

Cites Work

• Differential geometry in the large. Seminar lectures New York University 1946 and Stanford University 1956. With a preface by S. S. Chern
• A duality theorem for Willmore surfaces
• All constant mean curvature tori in \(R^ 3\), \(S^ 3\), \(H^ 3\) in terms of theta-functions
• Counterexample to a conjecture of H. Hopf
• On the mean curvature function for compact surfaces
• Constant mean curvature tori with spherical curvature lines in noneuclidean geometry
• On the classification of constant mean curvature tori
• Bonnet pairs and isothermic surfaces
• A characterization of tori with constant mean curvature in space form
• Constant mean curvature tori in terms of elliptic functions.
• Submanifolds of the MÖBIUS space, II FRENET Formulas and Curves of Constant Curvatures
• Unnamed Item

This page was built for publication: Non-special, non-canal isothermic tori with spherical lines of curvature