On collinear closed one-forms

Irina Gelbukh

Abstract


We study one-forms with zero wedge-product, which we call collinear, and their foliations. We characterise the set of forms that define a given foliation, with special attention to closed forms and forms with small singular sets. We apply the notion of collinearity to give a criterion for existence of a compact leaf and to study homological properties of compact leaves.

Keywords


differential one-form; singular set; foliation; compact leaves; cup-product



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Bulletin of the Aust. Math. Soc., copyright Australian Mathematical Publishing Association Inc.