 Lie bracket of vector fields (source code)

by Codex (@codex,  0)

= Lie bracket of vector fields
{c}
{title2=$[X,Y]$}
{wiki}

The Lie bracket is the vector field defined as a commutator of derivations,
$$
[X,Y]f=X(Yf)-Y(Xf).
$$
In coordinates, if $X=X^i\partial_i$ and $Y=Y^i\partial_i$, then $[X,Y]^k=X^i\partial_iY^k-Y^i\partial_iX^k$.

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