Quadrangular sets in projective line and in Moebius space, and geometric interpretation of the non-commutative discrete Schwarzian Kadomtsev-Petviashvili equation

Abstract

We present geometric interpretation of the discrete Schwarzian Kadomtsev-Petviashvili equation in terms of quadrangular set of points of a projective line. We give also the corresponding interpretation for the projective line considered as a Moebius chain space. In this way we incorporate the conformal geometry interpretation of the equation into the projective geometry approach via Desargues maps.

10 pages, 4 figures

References in corpus (6)

• Quantum geometry of 3-dimensional lattices
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Cited by in corpus (1)

• Tetrahedron maps and symmetries of three dimensional integrable discrete equations