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Abstract

We consider a diffeomorphism $G$ that acts between two Riemannian manifolds and examine the link between the structure of its Jacobian and the question whether $G$ conserves the module of a single foliation or the product of the modules of a system of foliations. We investigate sufficient conditions for the product of the modules of more than two foliations to be equal to 1 (which generalize the sufficient conditions regarding a pair of foliations, formulated by other authors). We show that these conditions emerge as a consequence of the sufficient conditions for the conservation of the product of modules.