Complex Dirac Structures: Invariants and Local Structure

We study complex Dirac structures, that is, structures in the complexified generalized tangent bundle. These include presymplectic foliations, transverse holomorphic CR-related geometries and structures. introduce two invariants, order (normalized) type. show that, together with real index, they allow us to obtain a pointwise classification of For constant order, we prove existence an underlying structure, which generalizes Poisson structure associated structure. index splitting theorem, gives local description terms leaf small transversal.