Solution
= 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 $R$).
= 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 $R$).