The lattice structure of connection preserving deformations for -Painlevé equations I.
The Lax integrable differential-difference dynamical systems on extended phase spaces.
The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI
Equivalence is established between a special class of Painlevé VI equations parametrized by a conformal dimension , time dependent Euler top equations, isomonodromic deformations and three-dimensional Frobenius manifolds. The isomonodromic tau function and solutions of the Euler top equations are explicitly constructed in terms of Wronskian solutions of the 2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by means of Grassmannian formulation. These Wronskian solutions give...
Transformations between surfaces in with flat normal and/or tangent bundles.
Transformations for hypersurfaces with vanishing Gauss-Kronecker curvature.
Tzitzeica-Bäcklund theorems.