# Constant scalar curvature with positive Ricci curvature

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?