A question on Foliated Manifolds

Hi

Let (M,F) be a foliated n dim. manifold s.t. there are only a finite
number of leaves with nontrivial holonomy, further assume that there
are n-1 independent vector fields X_1 ,X_2,X_3.......X_n-1 tangent to
the leaves,(naturally implies we have a codimension one foliation).

Is there any relation between the number of such nontrivial leaves and
some operator theoretical invariants of functional operators defined
by vector fields X_1 ,X_2,X_3.......X_n-1, in fact what is a
generalization of the following note?:

http://www.arxiv.org/abs/math.DS/0408037

Thank You

Ali Taghavi

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