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Riemann curvature tensor

Ricci tensor

{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 $R=n(n-1)K$.


Constant sectional curvature

Schur theorem in pseudo-Riemannian geometry

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

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

Constant sectional curvature ( $R_{ab c d} = K (g_{a c} g_{b d} - g_{a d} g_{b c})$ )

Schur theorem in pseudo-Riemannian geometry

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Constant sectional curvature (Rabcd​=K(gac​gbd​−gad​gbc​))

Schur theorem in pseudo-Riemannian geometry

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Constant sectional curvature ( $R_{ab c d} = K (g_{a c} g_{b d} - g_{a d} g_{b c})$ )

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