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arXiv · 0710.5820

The C-(symmetric) quadrilateral lattice, its transformations and the algebro-geometric construction

Adam Doliwa
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Abstract

The C-quadrilateral lattice (CQL), called also the symmetric lattice, provides geometric interpretation of the discrete CKP equation within the quadrilateral lattice (QL) theory. We discuss affine-geometric properties of the lattice emphasizing the role of the Gallucci theorem in the multidimensional consistency of the CQL. Then we give the algebro-geometric construction of the lattice. We also present the reduction of the vectorial fundamental transformation of the QL to the CQL case. In the Appendix we show a relation between the QL and the so called Darboux maps.

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Adam Doliwa. 2007-10-31. The C-(symmetric) quadrilateral lattice, its transformations and the algebro-geometric construction. https://doi.org/10.1016/j.geomphys.2010.01.005

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