Discrete special isothermic surfaces
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We discuss special isothermic nets of type \(N\), a new class of discrete isothermic nets, generalizing isothermic nets with constant mean curvature in spaceforms. In the case \(N=2\) these are the discrete analogues of Bianchi’s special isothermic surfaces that can be regarded as the origin of the rich transformation theory of isothermic surfaces. Accordingly, special isothermic nets come with Bäcklund transformations and a Lawson correspondence. The notion of complementary nets naturally occurs and sheds further light on the relation between geometry and integrability.
KeywordsIsothermic surface Darboux transformation Lawson correspondence Bäcklund transformation Polynomial conserved quantity Constant mean curvature
Mathematics Subject Classification53A10 53C42 53A30 37K25 37K35
The third author expresses his gratitude to Vienna University of Technology for financial support and their hospitality during the preparation of this paper. The figures in this text were created using Mathematica.
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