We show that symplectic forms taming complex structures on compact manifolds are related to special types of almost generalized Kähler structures. By considering the commutator [Q, Q] of the two associated almost complex structures J±, we prove that if either the manifold is 4-dimensional or the distribution ImQ is involutive, then the manifold can be expressed locally as a disjoint union of twisted Poisson leaves.
Tamed symplectic forms and Generalized Geometry
ENRIETTI, NICOLA;FINO, Anna Maria;
2013-01-01
Abstract
We show that symplectic forms taming complex structures on compact manifolds are related to special types of almost generalized Kähler structures. By considering the commutator [Q, Q] of the two associated almost complex structures J±, we prove that if either the manifold is 4-dimensional or the distribution ImQ is involutive, then the manifold can be expressed locally as a disjoint union of twisted Poisson leaves.
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