Structure of function algebras on foliated manifolds

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 $C_0(M)$ to the leaves in three partial cases. Also we consider a classification of the quasiinvariant measures and means on the leaves of $F$.