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VOL. 12 | 2011 Constant Mean Curvature Surfaces at the Intersection of Integrable Geometries
Aurea Quintino

Editor(s) Ivaïlo M. Mladenov, Gaetano Vilasi, Akira Yoshioka

Geom. Integrability & Quantization, 2011: 305-319 (2011) DOI: 10.7546/giq-12-2011-305-319


The constant mean curvature surfaces in three-dimensional space-forms are examples of isothermic constrained Willmore surfaces, characterized as the constrained Willmore surfaces in three-space admitting a conserved quantity. Both constrained Willmore spectral deformation and constrained Willmore Bäcklund transformation preserve the existence of a conserved quantity. The class of constant mean curvature surfaces in three-dimensional space-forms lies, in this way, at the intersection of several integrable geometries, with classical transformations of its own, as well as constrained Willmore transformations and transformations as a class of isothermic surfaces. Constrained Willmore transformation is expected to be unifying to this rich transformation theory.


Published: 1 January 2011
First available in Project Euclid: 13 July 2015

zbMATH: 1382.53005
MathSciNet: MR3087987

Digital Object Identifier: 10.7546/giq-12-2011-305-319

Rights: Copyright © 2011 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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