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Let $(M,g)$ be a riemannian manifold with riemannian curvature $R$. Then the Riemann-Ricci curvature is:

$$RR(X,Y)=tr(R(X,e_i)R(Y,e_i))$$

A Riemann-Einstein metric is such that:

$$RR(X,Y)=\lambda g(X,Y)$$

with $\lambda$ a scalar.

Can we have spherical solutions of the Riemann-Einstein?

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