Lecture 53 Vector fields and derivations

The goal of the last lectures is the Frobenius theorem that characterizes integrable distributions by k-planes on M. One of the main ingredients is the Lie bracket of two vector fields. In this lecture we identify vector fields and derivations. This is very useful to deal with the Lie bracket of two vector fields since, in particular, we can exploit this identification to obtain a simple intrinsic definition of the Lie bracket.

Lecture notes: