Monge-Ampere equations and generalized complex geometry. The two-dimensional case

Abstract

We associate an integrable generalized complex structure to each 2-dimensional symplectic Monge-Ampère equation of divergent type and, using the Gualtieri $\bar{\partial }$ operator, we characterize the conservation laws and the generating function of such equation as generalized holomorphic objects.

References in corpus (8)

• Generalized complex geometry
• Instantons, Poisson structures and generalized Kaehler geometry
• Geometry of Hyper-Kähler Connections with Torsion
• New aspects of the ddc-lemma
• Generalized geometry and the Hodge decomposition
• Generalized complex structures and Lie brackets
• Potentials for hyper-Kahler metrics with torsion
• Submanifolds of generalized complex manifolds

Cited by in corpus (3)

• On a class of integrable systems of Monge-Ampère type
• Monge-Ampère Structures and the Geometry of Incompressible Flows
• Complex solutions of Monge-Ampère equations