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Let $(M,g)$ be a riemannian manifold with riemannian curvature $R$, then I call $M$ a Riemann manifold if $g$ is such that, with $r(X,Y,Z,T)=g(R(X,Y)Z,T)$:

$$tr(R(X,Y)R(Z,T))= \lambda r(X,Y,Z,T)$$

with $\lambda$ a scalar.

Are there non trivial examples of such Riemann manifolds?

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