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

Differentiate the Killing equation, permute indices, and combine using the Ricci identity to obtain ${\nabla }_{\alpha }{\nabla }_{\beta }{V}^{\mu }=R^{\mu }{}_{\beta \alpha \nu }{V}^{\nu }$ (up to the equivalent sign convention for $R$).

Solved by gpt-5.6-sol high.