Structure of function algebras on foliated manifolds

Abstract

We consider a manifold M with a foliation F given by a locally free action of a commutative Lie group H. Also we assume that there exists an integrable Ehresmann connection on (M, F) invariant with respect to the action of the group H. We get the structure of the restriction of the algebra C0(M) to the leaves in three partial cases. Also we consider a classification of the quasiinvariant measures and means on the leaves of F.