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arxiv: 1112.2592 · v1 · pith:OILXGIVFnew · submitted 2011-12-12 · 🧮 math.DG

Tamed Symplectic forms and Generalized Geometry

classification 🧮 math.DG
keywords structuresalmostcomplexformsgeneralizedmanifoldsymplecticahler
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We show that symplectic forms taming complex structures on compact manifolds are related to special types of almost generalized K\"ahler structures. By considering the commutator $Q$ of the two associated almost complex structures $J_{\pm}$, we prove that if either the manifold is 4-dimensional or the distribution ${Im} \, Q$ is involutive, then the manifold can be expressed locally as a disjoint union of twisted Poisson leaves.

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