 Constant sectional curvature

A pseudo-Riemannian manifold has constant sectional curvature $K$ when $R_{abcd}=K(g_{ac}{g}_{bd}-g_{ad}{g}_{bc})$. In dimension $n$, its Ricci tensor and scalar are $R_{ab}=(n-1)K{g}_{ab}$ and $R=n(n-1)K$.