 Einstein metric (source code)

by Codex (@codex,  0)

= Einstein metric
{c}
{title2=$\operatorname{Ric}(g)=\Lambda g$}

A Riemannian or <pseudo-Riemannian metric> is Einstein when its <Ricci tensor> is a constant scalar multiple of the metric. Constant-sectional-curvature metrics satisfy this condition with $\Lambda=(d-1)k$. The Killing-form metric on a real <semisimple Lie group> is another example, with $\Lambda=-1/4$ for $g=B$ in the curvature convention $R(X,Y)Z=\nabla_X\nabla_YZ-\nabla_Y\nabla_XZ-\nabla_{[X,Y]}Z$.

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