Holomorphic vector fields transverse to polydiscs

In this article, we study holomorphic vector fields transverse to the boundary of a polydisc in C^n, n >= 3. We prove that, under a suitable hypothesis of transversality with the boundary of the polydisc, the foliation is the pull-back of a linear hyperbolic foliation via a locally injective holomorphic map. This is the n >=, 3 version for one-dimensional foliations of a previous result proved for n = 2 by Brunella and Sad and for codimension-one foliations by Ito and Scardua.