A Darboux theorem for multi-symplectic manifolds (Q1122843)

The author studies a class of geometric structures (called multi- symplectic ones) defined by \(i+1\)-forms in a manner analogous to the definition of the symplectic structure by 2-forms (the \(i+1\)-forms mentioned above may be constructed e.g. on i-forms bundle over appropriate jet bundle in analogy with the construction of the canonical 2-form on a cotangent bundle). An extension of Darboux-Moser-Weinstein theorem is proved for these structures, a characterization of the pseudogroups determined by these structures is given. The author notes some problems of mathematical physics where such structures have naturally arisen.