Constant mean curvature surfaces at the intersection of integrable geometries

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


The constant mean curvature surfaces in three-dimensional spaceforms 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 threedimensional 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.
Original languageEnglish
Title of host publicationGeometry, Integrability and Quantization
EditorsI.M. Mladenov, G. Vilasi, A. Yoshioka
PublisherBulgarian Academy of Sciences, Institute of Biophysics and Biomedical Engineering
Number of pages15
Publication statusPublished - 2011


Dive into the research topics of 'Constant mean curvature surfaces at the intersection of integrable geometries'. Together they form a unique fingerprint.

Cite this