Lie derivatives are discussed in this brief chapter, which I have included in part because it is so traditional. There are two more concrete reasons for this diversion. The first is that Lie derivatives offer some sort of introduction to the idea behind the Frobenius theorem. The second is that they give us an inadequate way of transporting vectors along curves. Why inadequate? This is a technicality, difficult to describe for now. But what we really need to transport vectors in a “parallel” manner is a connection. This is what a connection will do for us. I also discuss why integral curves are not always so important in physics. But be warned that my point of view here is rather heretical.
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