Global solvability for a class of overdetermined systems |
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| Authors: | Adalberto P Bergamasco Alexandre Kirilov |
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| Institution: | a Departamento de Matemática, ICMC-USP, Caixa Postal 668, São Carlos, SP 13560-970, Brazil
b Departamento de Matemática, UFPR, Caixa Postal 19081, Curitiba, PR 81531-990, Brazil |
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| Abstract: | 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. |
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| Keywords: | Global solvability Overdetermined systems Complex vector fields |
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