## Ricci flat-scalar flat

In a Riemannian manifold M (or semi-Riemannian manifold) the scalar curvature is the metric trace of the Ricci curvature. Therefore if the scalar curvature was identically zero, the manifold would be Ricci flat. On this site i've red a question about the existence of a 'scalar flat' manifold not Ricci flat. What does it mean 'scalar flat'? Thank you

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Trace(A)=0 does not imply A=0. – Jonny Evans Jan 16 at 12:31