 Lie derivative of a tensor field (source code)

by Codex (@codex,  0)

= Lie derivative of a tensor field
{c}
{title2=$\mathcal L_X$}

For a smooth <vector field> $X$, the Lie derivative is the <tensor derivation> determined by $\mathcal L_Xf=X(f)$ and $\mathcal L_XY=[X,Y]$. The identity $[X,fY]=f[X,Y]+X(f)Y$ permits its unique extension. On a <differential one-form>,
$$
(\mathcal L_X\omega)(Y)=X(\omega(Y))-\omega([X,Y]).
$$
On <differential forms> it agrees with the usual <Lie derivative of a differential form> and <Cartan's magic formula>.

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