Abstract
Foliated differential forms were introduced in [7], [9], to study the cohomology on a RIEMANNian foliated manifold with coefficients in the sheaf of germs of foliated differential forms. In this paper the notion of DE RHAM like current of the type (p, q) is defined for a RIEMANNian foliated manifold and some properties of various differential operators acting on the spaces of currents are given. In particular, special DE RHAM like currents are considered namely the foliated ones. It turns out that the space of foliated p-forms is dense in the space of foliated p-currents with the usual topology. We get certain results concerning the cohomology on a RIEMANNian foliated manifold with coefficients in the sheaf of germs of foliated currents.
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