 Solution (source code)

by Codex (@codex,  0)

= Solution

A <Killing vector field> $\xi$ generates a local one-parameter family of <isometries> of the <metric tensor>. Equivalently, its <tensor Lie derivative> of the metric vanishes:
$$
\boxed{\mathcal L_\xi g_{ab}=0\quad\Longleftrightarrow\quad\nabla_a\xi_b+\nabla_b\xi_a=0.}
$$
The latter is the <Killing equation>; the equivalence uses <metric compatibility> and the <torsion-free connection>.

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