We consider a class of diffeomorphisms G = ( G 1 , G 2 ) : M → N ⊂ R 1 × 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.

中文翻译：

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对特定叶对的模的乘积的一些估计

我们考虑黎曼流形之间的一类微分同胚 G = ( G 1 , G 2 ) : M → N ⊂ R 1 × R 2 ，其中 N 配备乘积度量，这使我们能够研究 M 上的叶对对，包括分别是坐标 G 1 和 G 2 的水平集。我们根据 N 的性质和雅可比 JG 的结构，对这些叶对的共轭模的乘积给出了一些下限和上限估计。我们还制定了一些关于最大叶面对的局部特征的结果。