(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let M be a differentiable manifold. Let X and Y be two vector fields on M, and let t be a tensor field on M. Prove

[itex] \mathcal{L}_{[X,Y]}t = \mathcal{L}_X\mathcal{L}_Yt -\mathcal{L}_Y\mathcal{L}_Xt[/itex]

2. Relevant equations

All is fair game, though presumably a coordinate-free description is superior to one in local coordinates.

3. The attempt at a solution

I've tried working it out in local coordinates, but, because we need to show that the statement holds for a general tensor field of any type, the algebra gets very hairy very quickly. Any suggestions are much appreciated.

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# Differential Geometry: Lie derivative of tensor fields.

Can you offer guidance or do you also need help?

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