 Constant sectional curvature (source code)

by Codex (@codex,  0)

= Constant sectional curvature
{title2=$R_{abcd}=K(g_{ac}g_{bd}-g_{ad}g_{bc})$}
{wiki}

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 $R_{ab}=(n-1)Kg_{ab}$ and $R=n(n-1)K$.

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