Abstract
Consider a symplectic form ω and a closed 2-form ω1 on a real or complex manifold. Suppose that the Nijenhuis torsion of the tensor fieldJ defined by ω1(X,Y) = ω(JX,Y) vanishes. In this paper we give the complete local classification of the couple {ω, ω1} on a dense open set, defined by some minor conditions of regularity. Around each point of this open set we can find coordinates on wich ω is written with constant coefficients and ω1 with affine ones.
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