Some Estimates for the Product of Modules of Specific Pairs of Foliations

Abstract

We consider a class of diffeomorphisms G = (G1, G2) : MNR1 × R2 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 G1 and G2, 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.

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Correspondence to A. Kaźmierczak.

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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 3, pp. 594–606.

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Kaźmierczak, A. Some Estimates for the Product of Modules of Specific Pairs of Foliations. Sib Math J 61, 468–477 (2020). https://doi.org/10.1134/S0037446620030088

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Keywords

  • foliation
  • module
  • capacity
  • submersion