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Singular foliations and differential \(p\)-forms. (English) Zbl 0997.58001

The notion of integrable differential \(p\)-form is introduced in order to present an adequate analytic object to study the structure of the codimension \(p\) singular foliations. After a preliminary section, in section 2 there are described completely the foliations induced by linear integrable \(p\)-forms on \(K^n\) \((K=\mathbb{R},\mathbb{C})\) and in section 3 there are given the main results on the local structure of plane fields and on the local structure of foliations. Finally, the validity of the results established in sections 2 and 3 is discussed in the context of real analytic, and class \(C^r\), \(p\)-forms and the extension for holomorphic foliations of the complex projective space is presented.

MSC:

58A10 Differential forms in global analysis
32S65 Singularities of holomorphic vector fields and foliations
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