Global solvability for involutive systems on the torus

Abstract

In this article, we consider a class of involutive systems of n smooth vector fields on the torus of dimension n+1. We prove that the global solvability of this class is related to an algebraic condition involving Liouville forms and the connectedness of all sublevel and superlevel sets of the primitive of a certain 1-form associated with the system.

Keywords

• Global solvability
• involutive systems
• complex vector fields
• Liouville number