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**Constant mean curvature surfaces at the intersection of integrable geometries.**
*(English)*
Zbl 1382.53005

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 12th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 4–9, 2010. Sofia: Bulgarian Academy of Sciences. Geometry, Integrability and Quantization, 305-319 (2011).

Summary: 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.

For the entire collection see [Zbl 1245.00049].

For the entire collection see [Zbl 1245.00049].