First-order invariants of differential 2-forms

Abstract

Let M be a smooth manifold of dimension 2n, and let OM be the dense open subbundle in _^²T*M of 2-covectors of maximal rank. The algebra of Diff M-invariant smooth functions of rst order on OM is proved to be isomorphic to the algebra of smooth Sp(Ω_x)-invariant functions on ^³T_x^*M, x being axed point in M, and Ω_x a fixed element in (O_M)x. The maximum number of functionally independent invariants is computed.