Let $M$ be a compact smooth manifold and $g$ a Riemannian metric on $M$.

By the solution of the Yamabe problem, there exists a metric $\tilde{g}$ of constant scalar curvature on $M$ which is conformal to $g$.

Suppose $g$ has positive Ricci curvature. Does there exist a metric $\tilde{g}$ conformal to $g$ such that $\tilde{g}$ has constant scalar curvature and positive Ricci curvature as well?


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