Global solvability for a class of overdetermined systems

In this work we consider systems of two smooth vector fields on the three-dimensional torus associated to a closed 1-form. We prove that, for such systems, the global solvability in the space of smooth functions is characterized by the property of all the sublevel and superlevel sets of a certain primitive of the 1-form being connected. © 2007 Elsevier Inc. All rights reserved