The complex Frobenius theorem for rough involutive structures

We establish a version of the complex Frobenius theorem in the context of a complex subbundle \mathcal {S} of the complexified tangent bundle of a manifold having minimal regularity. If the subbundle \mathcal {S} defines the structure of a Levi-flat CR-manifold, it suffices that \mathcal {S} be Lips...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2007-01, Vol.359 (1), p.293-322
Main Authors: Hill, C. Denson, Taylor, Michael
Format: Article
Language:English
Subjects:
Analytic functions
Coordinate systems
Exact sciences and technology
Family structure
Logical givens
Mathematical analysis
Mathematical manifolds
Mathematical theorems
Mathematics
Partial differential equations
Sciences and techniques of general use
Tangents
Tensors
Vector fields
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Summary:We establish a version of the complex Frobenius theorem in the context of a complex subbundle \mathcal {S} of the complexified tangent bundle of a manifold having minimal regularity. If the subbundle \mathcal {S} defines the structure of a Levi-flat CR-manifold, it suffices that \mathcal {S} be Lipschitz for our results to apply. A principal tool in the analysis is a precise version of the Newlander-Nirenberg theorem with parameters, for integrable almost complex structures with minimal regularity, which builds on recent work of the authors.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-06-04067-0