Integral formulae for foliations with singularities

Paweł Walczak¹

¹ Katedra Geometrii Wydział Matematyki i Informatyki Uniwersytet Łódzki Banacha 22 90-238 Łódź, Poland

Colloquium Mathematicum, Tome 150 (2017) no. 1, pp. 141-148

Résumé

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).

Détail

DOI : 10.4064/cm7105s-12-2016

Keywords: consider oriented closed riemannian manifold equipped codimension one foliation mathcal defined outside finite union varsigma pairwise disjoint closed submanifolds sufficiently large codimension using technical lemma several integral formulae known foliations closed manifolds under conditions integrability functions particular results article generalize observations andrzejewski czyk walczak rovenski walczak