Simultaneous local classification of two compatible symplectic forms. (Classification locale simultanée de deux formes symplectiques compatibles.) (French) Zbl 0807.53028
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.
Reviewer: G.V.Khmelevskaja-Plotnikova (Namur)
MSC:
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
Keywords:
compatible symplectic forms; closed forms; symplectic form; complex manifold; Nijenhuis torsionReferences:
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