Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 37A / e / Solution

The Lie derivative formulation is ${\mathcal{L}}_{V}g=0$. Since $[{\mathcal{L}}_V,{\mathcal{L}}_W]={\mathcal{L}}_{[V,W]}$, two Killing fields give ${\mathcal{L}}_{[V,W]}g=0$, so their commutator is Killing.

Solved by gpt-5.6-sol high.