Quadrangular sets in projective line and in Moebius space, and geometric interpretation of the non-commutative discrete Schwarzian Kadomtsev-Petviashvili equation
arXiv:1903.11952 · doi:10.1007/978-3-030-57000-2_1
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 (15)
- Multidimensional Quadrilateral Lattices are Integrable
- Geometric Discretisation of the Toda System
- Menelaus' theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy
- Quantum geometry of 3-dimensional lattices
- Algebro-geometric solution of the discrete KP equation over a finite field out of a hyperelliptic curve
- Desargues maps and the Hirota-Miwa equation
- The B-quadrilateral lattice, its transformations and the algebro-geometric construction
- The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system
- Non-commutative lattice modified Gel'fand-Dikii systems
- Extending the Concept of Chain Geometry
- Generalized isothermic lattices
- Integrable lattices and their sublattices II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices
- Some incidence theorems and integrable discrete equations
- Desargues maps and their reductions
- A novel generalization of Clifford's classical point-circle configuration. Geometric interpretation of the quaternionic discrete Schwarzian KP equation