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Conservation of module and the product of modules of foliations

Volume 124 / 2020

Anna Kaźmierczak Annales Polonici Mathematici 124 (2020), 161-172 MSC: Primary 58C25; Secondary 58C35, 30C35, 53C12. DOI: 10.4064/ap190101-10-6 Published online: 21 February 2020

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.

Authors

  • Anna KaźmierczakFaculty of Mathematics and Computer Science
    University of Lodz
    Banacha 22
    90-238 Łódź, Poland
    e-mail

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