Asymptotic lattices and their integrable reductions I: the Bianchi and the Fubini-Ragazzi lattices
Abstract
We review recent results on asymptotic lattices and their integrable reductions. We present the theory of general asymptotic lattices in R3 together with the corresponding theory of their Darboux-type transformations. Then we study the discrete analogues of the Bianchi surfaces and their transformations. Finally, we present the corresponding theory of the discrete analogues of the isothermally-asymptotic (Fubuni-Ragazzi) nets.
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