Proceedings of the International Conference on Geometry, Integrability and Quantization

Constant Mean Curvature Surfaces at the Intersection of Integrable Geometries

Aurea Quintino

Abstract

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.

Article information

Source
Proceedings of the Twelfth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Gaetano Vilasi and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2011), 305-319

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436815629

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

Mathematical Reviews number (MathSciNet)
MR3087987

Zentralblatt MATH identifier
1382.53005

Citation

Quintino, Aurea. Constant Mean Curvature Surfaces at the Intersection of Integrable Geometries. Proceedings of the Twelfth International Conference on Geometry, Integrability and Quantization, 305--319, Avangard Prima, Sofia, Bulgaria, 2011. doi:10.7546/giq-12-2011-305-319. https://projecteuclid.org/euclid.pgiq/1436815629


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