ar X iv : n lin / 0 61 10 18 v 2 [ nl in . S I ] 1 1 N ov 2 00 6 GENERALIZED ISOTHERMIC LATTICES
نویسنده
چکیده
We study multidimensional quadrilateral lattices satisfying simultaneously two inte-grable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Möbius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constraint imposed on the (complex) cross-ratio of the circular lattice. We derive the analogous condition for our generalized isthermic lattices using Steiner's projective structure of conics and we present basic geometric constructions which encode integrability of the lattice. In particular we introduce the Darboux transformation of the generalized isothermic lattice and we derive the corresponding Bianchi permutability principle. Finally, we study two dimensional generalized isothermic lattices, in particular geometry of their initial boundary value problem.
منابع مشابه
ar X iv : n lin / 0 61 10 18 v 3 [ nl in . S I ] 6 J an 2 00 7 GENERALIZED ISOTHERMIC LATTICES
We study multidimensional quadrilateral lattices satisfying simultaneously two inte-grable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Möbius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constrain...
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