suppose there is a vector field V on a manifold M(adsbygoogle = window.adsbygoogle || []).push({});

V generates a flow on M

suppose \gamma(t) is an integral curce in this flow

now there is another vector field W on M

why not define the lie derivative of W with respect to V as the limit of the divide

(W(\gamma+\delta \gamma)-W(\gamma))/\delta \gamma

here the difference is taken by components

i think this is very natural from our experience in the calculus course in undergraduate.

why we need to drag?

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# Defition of lie derivatives

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