• DOI:10.7546/giq-12-2011-305-319
• Corpus ID: 125011493

Constant Mean Curvature Surfaces at the Intersection of Integrable Geometries

@inproceedings{Quintino2011ConstantMC,
  title={Constant Mean Curvature Surfaces at the Intersection of Integrable Geometries},
  author={{\'A}urea Casinhas Quintino},
  year={2011}
}

• Á. Quintino
• Published 2011
• Mathematics

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 Backlund 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.