ON LOCAL REDUCTION THEOREMS FOR SINGULAR SYMPLECTIC FORMS ON A 4-DIMENSIONAL MANIFOLD

摘要

We study local invariants of singular symplectic forms with structurally smooth Martinet hypersurfaces on a 4-dimensional manifold M. We prove that the equivalence class of a germ at p 6 M of a singular symplectic form ui is determined by the Martinet hypersurface, the canonical orientation of it, the pullback of the singular symplectic form to it and the 2-dimensional kernel of u> at p. We also show which germs of closed 2-forms on a 3-dimensional subman-ifbld can be realizable as pullbacks of singular symplectic forms to structurally smooth Martinet hypersurfaces.