Some estimates for the product of modules of specific pairs of foliations

We consider a class of diffeomorphisms $G=(G_1,G_2):M\rightarrow N\subset R_1\times R_2$ between Riemannian manifolds, where $N$ is equipped with the product metric, which allows us to investigate the pairs of foliations on $M$ consisting of level sets of coordinates $G_1$ and $G_2$, respectively. We give some lower and upper estimates for the product of conjugate modules of these pairs of foliations that depend on the properties of $N$ and the structure of the Jacobian $JG$. We also formulate a few results on the local features of maximal pairs of foliations.