Einstein manifold
= Einstein manifold
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{title2=$\operatorname{Ric}=\Lambda g$}
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An <Einstein manifold> has <Ricci curvature> equal to a constant multiple of its metric. In the Riemannian setting, the round unit sphere has $\Lambda=n-1$. This condition is weaker than constant <sectional curvature> in higher dimensions. The definition can also be applied to pseudo-Riemannian metrics, but positivity is assumed in the completeness theorems discussed here.