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Monge-Ampere equations and generalized complex geometry. The two-dimensional case
We associate an integrable generalized complex structure to each
2-dimensional symplectic Monge-Amp\`ere equation of divergent type and, using
the Gualtieri operator, we characterize the conservation laws
and the generating function of such equation as generalized holomorphic
objects
Complex solutions of Monge-Amp\`ere equations
We describe a method to reduce partial differential equations of
Monge-Amp\`ere type in 4 variables to complex partial differential equations in
2 variables. To illustrate this method, we construct explicit holomorphic
solutions of the special lagrangian equation, the real Monge-Amp\`ere equations
and the Plebanski equations.Comment: 16 pages, 5 tables To appear in Journal of Geometry and Physic
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