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A Frobenius Theorem for Corank-1 Continuous Distributions in Dimensions two and three

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arxiv 1411.5896 v5 pith:MRWGOO2C submitted 2014-11-21 math.DG math.APmath.DS

Stefano Luzzatto , Sina Tureli , Khadim War This is my paper · ORCID
classification math.DGmath.APmath.DS
keywords theoremcontinuouscorank-1dimensionsdistributionsfrobeniusthreeasymptotic
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We formulate a notion of (uniform) asymptotic involutivity and show that it implies (unique) integrability of corank-1 continuous distributions in dimensions three or less. This generalizes and extends a classical theorem of Frobenius Theorem which says that an involutive C^1 distribution is uniquely integrable.

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