7. Vector fields
We begin this lecture by introducing the Einstein Summation Convention. This may at first seem like more effort than it’s worth, but I guarantee by the end of the course you will be thankful for it!
We then define vector fields as smooth sections of the tangent bundle, and define the Lie bracket of two vector fields. We define a Lie algebra and show that the space of vector fields forms an infinite-dimensional Lie algebra.
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