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 ∧² T*M of 2-covectors of maximal rank. The algebra of Diff M -invariant smooth functions of first order on OM is proved to be isomorphic to the algebra of smooth Sp(Ωx)-invariant functions on , x being a fixed point in M , and Ωx a fixed element in (OM ) _x . The maximum number of functionally independent invariants is computed.