Generalizations of Frobenius' Theorem on Manifolds and Subcartesian Spaces

• Autores: Jedrzej Sniatycki
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 50, Nº 3, 2007, págs. 447-459
• Idioma: inglés
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• Resumen

  • Let mathcal{F} be a family of vector fields on a manifold or a subcartesian space spanning a distribution D. We prove that an orbit O of mathcal{F} is an integral manifold of D if D is involutive on O and it has constant rank on O. This result implies Frobenius' theorem, and its various generalizations, on manifolds as well as on subcartesian spaces.