Integral formulae for foliations with singularities
Volume 150 / 2017
Colloquium Mathematicum 150 (2017), 141-148
MSC: Primary 53C12; Secondary 57R30.
DOI: 10.4064/cm7105s-12-2016
Published online: 28 July 2017
Abstract
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).
