Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2003-12-02
Nonlinear Sciences
Exactly Solvable and Integrable Systems
26 pages, 7 postscript figures
Scientific paper
10.1016/j.geomphys.2004.02.010
We introduce the dual Koenigs lattices, which are the integrable discrete analogues of conjugate nets with equal tangential invariants, and we find the corresponding reduction of the fundamental transformation. We also introduce the notion of discrete normal congruences. Finally, considering quadrilateral lattices "with equal tangential invariants" which allow for harmonic normal congruences we obtain, in complete analogy with the continuous case, the integrable discrete analogue of the Bianchi system together with its geometric meaning. To obtain this geometric meaning we also make use of the novel characterization of the circular lattice as a quadrilateral lattice whose coordinate lines intersect orthogonally in the mean.
Doliwa Adam
Nieszporski Maciej
Santini Paolo Maria
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