Distributions and Foliations

Abstract

Given a nonvanishing vector field on a smooth manifold M, the results of Chapter 9show that the integral curves of the vector field fill up M and fit together nicely like parallel lines in Euclidean space. In this chapter we explore an important generalization of this idea to higher-dimensional submanifolds. Given a smooth subbundle of the tangent bundle of M, called a distribution on M, we can ask whether there are