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Cohomology on a Riemannian foliated manifold with coefficients in the sheaf of germs of foliated currents
Author(s) -
Craioveanu Mircea,
Puta Mircea
Publication year - 1980
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19800990106
Subject(s) - mathematics , sheaf , pure mathematics , cohomology , manifold (fluid mechanics) , riemannian manifold , differential form , de rham cohomology , exponential map (riemannian geometry) , mathematical analysis , geometry , equivariant cohomology , scalar curvature , sectional curvature , engineering , curvature , mechanical engineering
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.