Monge-Ampère equations and generalized complex geometry - The two-dimensional case

Bertrand Banos (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

We associate an integrable generalized complex structure to each 2-dimensional symplectic Monge-Ampère 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.

Mots clés: Geometry of PDE; Monge-Ampère equations; Generalized complex geometry; differential forms

Domaines: Géométrie différentielle [math.DG]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Bertrand Banos. Monge-Ampère equations and generalized complex geometry - The two-dimensional case. Journal of Geometry and Physics, 2007, 57, pp.841-853. ⟨10.1016/j.geomphys.2006.06.005⟩. ⟨hal-01308407⟩