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Sur les singularités des formes différentielles. (French) Zbl 0189.10001
In this paper, the singularities of exterior differential forms on a manifold are studied from a view-point analogous to the classical theory of singularities of differentiable mappings. The main invariants considered are the rank and the class (in E. Cartan’s sense) of an exterior differential form. The generic behaviour of these invariants is studied by means of the transversality theorems. For instance, the set of points of a \(n\)-dimensional manifold, where the class of a one-form is \(n-c\), is generically a regular submanifold of codimension \({c(c+1)\over 2}\). Higher order singularities are studied in some detail in the case of low dimensions (1-forms in 3 dimensions and 2-forms in 4 dimensions). Then is proved the existence of models for the simplest singularities of 1-forms and closed 2-forms.
Reviewer: J. Martinet

MSC:
58A15 Exterior differential systems (Cartan theory)
58K99 Theory of singularities and catastrophe theory
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