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Commutation relations between covariant and Lie derivatives

I am currently working on extrinsic riemannian geometry and I am looking for a sort of commutation relation between the covariant and Lie derivatives.To be more precise : considering an hypersurface $H...

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Answer by Didier for Commutation relations between covariant and Lie derivatives

I recently answered my question by finding a formula I wasn't aware of.Let $\nabla$ be a connexion and $X$ a vector field. Then $\mathcal{L}_X\nabla$ is a tensor and\begin{align}\mathcal{L}_X\nabla...

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