In pseudo-Riemannian geometry it is well known that every three-dimensional Einstein manifold has constant curvature. A proof of this is sketched [here](https://math.stackexchange.com/a/2194463/242708).


**Question**. Does anyone know where in the literature I can find a proof of such result?



Proof that every three-dimensional Einstein manifold has constant curvature
This is precisely Proposition 1.120 on p.49 in Besse's "Einstein Manifolds" (I am using the reprint of the 1987 edition, so the numbering may be different in the older edition):



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> A 3-dimensional pseudo-Riemannian manifold is Einstein iff it has constant (sectional) curvature.
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Note that the proof is before the proposition.


