Global solutions to involutive systems

Global solutions to involutive systems

In this work we consider a class of systems of two vector fields on the 3-torus associated to a closed smooth complex 1-form c=a+ib exact. Necessary conditions and sufficient conditions for this system to be globally solvable are provided in terms of the position of the global extrema and the connec...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2015-11, Vol.143 (11), p.4851-4862
Hauptverfasser: BERGAMASCO, A. P., KIRILOV, A., NUNES, W. V. L., ZANI, S. L.
Format: Artikel
Sprache:eng
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Zusammenfassung:In this work we consider a class of systems of two vector fields on the 3-torus associated to a closed smooth complex 1-form c=a+ib exact. Necessary conditions and sufficient conditions for this system to be globally solvable are provided in terms of the position of the global extrema and the connectedness of sublevel and superlevel sets of the primitives of b.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/12633