Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 309 / 1 / b / Solution

Contract the isotropic-curvature formula on $a,c$. In dimension $n$ it givesSubstitution into the contracted Bianchi identity givesSince $n>2$, ${\nabla }_{b}K=0$, so $K$ is constant on each connected component. Thus this is constant sectional curvature, withThis argument is Schur theorem in pseudo-Riemannian geometry.