Simultaneous local classification of two compatible symplectic forms
Consider a symplectic form \(\omega\) and a closed 2-form \(\omega_ 1\) on a real or complex manifold. Supposing that Nijenhuis torsion of the tensor field \(J\) defined by \(\omega_ 1 (X,Y) = \omega (JX,Y)\) vanishes, one gives the complete local classification of the \(\{\omega, \omega_ 1\}\) on a dense open set with some conditions of regularity. Each regular point of this set has a neighborhood such that it is possible to find coordinates in order to write \(\omega\) with constant coefficients and \(\omega_ 1\) with affine ones.
scientific article; zbMATH DE number 572232
scientific article