On complex codimension-one foliations transverse fibrations

We study codimension-one holomorphic foliations which are transverse to fibrations and, therefore, are conjugate to suspensions of groups of Mobius transformations. For the general case, we assume that there exists an invariant transverse measure. The existence of such an invariant transverse measure is proved for the case where there is a leaf with the subexponential growth or the basis has an amenable fundamental group. This result applies, e.g., for the study of amenable Lie group actions on complex projective spaces.