Certain closed quasi-Einstein manifolds are rigid, reducing to Einstein metrics, via a curvature identity tied to the Ricci flow.
Besse,Einstein manifolds, Classics in Mathematics, Springer-Verlag, Berlin, 2008, Reprint of the 1987 edition
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Quasi-Einstein Metrics and a curvature identity associated with the Ricci flow
Certain closed quasi-Einstein manifolds are rigid, reducing to Einstein metrics, via a curvature identity tied to the Ricci flow.