On the global solvability for overdetermined systems

Bergamasco, Adalberto; Kirilov, Alexandre; Nunes, Wagner; Zani, Sérgio

doi:10.1090/S0002-9947-2012-05414-6

On the global solvability for overdetermined systems
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by Adalberto P. Bergamasco, Alexandre Kirilov, Wagner Vieira Leite Nunes and Sérgio Luís Zani PDF

Trans. Amer. Math. Soc. 364 (2012), 4533-4549 Request permission

Abstract:

We consider a class of systems of two smooth vector fields on the 3-torus associated to a closed 1-form. We prove that the global solvability is completely determined by the connectedness of the sublevel and superlevel sets of a primitive of this 1-form in the minimal covering.

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