A class of globally non-solvable involutive systems on the torus

摘要

We consider an involutive system associated with a smooth and closed 1-form defined on the n-dimensional torus. We show the non-global solvability of the system by assuming a certain geometric condition on the global primitive of the imaginary part of this 1-form. We use this result to characterize completely the global solvability of certain partially coupled systems.