Fibrations en tores et n-formes de Liouville en dimension 2n

Abstract

In this work we prove a kind of Arnold–Liouville theorem for n-forms ω in dimension 2n, whose local model is $\text{ω=∑}{}_{\mathrm{j=1}}{}^{\mathrm{n}}\text{d}\text{y}{}_{\mathrm{j}}\text{∧}\text{d}\text{x}{}_1\text{∧⋯∧}\text{d}\text{̂}\text{x}{}_{\mathrm{j}}\text{∧⋯∧}\text{d}\text{x}{}_{\mathrm{n}}$. Some global aspects of these forms are studied as well.