## 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

### Keywords:

singular foliation; integrable differential form
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### References:

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