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Integral formulae for foliations with singularities

Volume 150 / 2017

Paweł Walczak Colloquium Mathematicum 150 (2017), 141-148 MSC: Primary 53C12; Secondary 57R30. DOI: 10.4064/cm7105s-12-2016 Published online: 28 July 2017


We consider an oriented closed Riemannian manifold $M$ equipped with a codimension-one foliation ${\mathcal F}$ defined outside a finite union $\varSigma $ of pairwise disjoint closed submanifolds of sufficiently large codimension. Using a technical lemma we show that several integral formulae known for foliations of closed manifolds hold also in this case under some conditions (integrability of some functions). In particular, the results of this article generalize some observations of Andrzejewski et al. (2014), Lużyńczyk and Walczak (2015) and Rovenski and Walczak (2012).


  • Paweł WalczakKatedra Geometrii
    Wydział Matematyki i Informatyki
    Uniwersytet Łódzki
    Banacha 22
    90-238 Łódź, Poland

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