Differential geometry and canonical reductions of the 4+4-dimensional TED equation
Boris Konopelchenko (Univ. of Salento)
It is shown that the natural geometric setting of the integrable 4+4-dimensional TED equation is a particular Kahlerian tangent bundle of an affine manifold. The multi-dimensional consistency of this equation is straightforward in this context. Various classes of the integrability-preserving reductions of the TED equation and their geometry are considered. Such reductions include, in particular, the heavenly type equations, governing the self-dual Einstein spaces, and their "integrable" deformations.
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