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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...
We prove that the Lie algebra of infinitesimal automorphisms of the transverse structure on the total space of the transverse bundle of a foliation is isomorphic to the semi-direct product of the Lie algebra of the infinitesimal automorphism of the foliation by the vector space of the transverse vector fields. The derivations of this algebra are entirely determined and we prove that this Lie algebra characterises the foliated structure of a compact Hausdorff foliation.
The aim of this paper is to determine explicitly the algebraic structure of the curvature algebra of the 3-dimensional Heisenberg group with left invariant cubic metric. We show, that this curvature algebra is an infinite dimensional graded Lie subalgebra of the generalized Witt algebra of homogeneous vector fields generated by three elements.
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