An analogue of the holonomy bundle for a foliated manifold
Let \({\mathcal F}\) be a smooth foliation of the connected manifold M and let D be a distribution on M complementary to the tangent bundle of \({\mathcal F}\). For each \(x\in M\), let P(x) be the set of points in M which can be reached from x by a piecewise smooth curve tangent to D. We show that under certain geometric conditions the sets P(x) are immersed submanifolds of M. As a special case we consider the situation in which M is a Riemannian manifold and D is the distribution orthogonal to the leaves.
scientific article; zbMATH DE number 4028328