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Consider a compact Lie group $G$ and a closed subgroup $H<G$. Suppose$\mathcal M$ is the set of $G$-invariant Riemannian metrics on the homogeneousspace $M=G/H$. We obtain a sufficient condition for the existence of$g\in\mathcal M$ and $c>0$ such that the Ricci curvature of $g$ equals $cT$ fora given $T\in\mathcal M$. This condition is also necessary if the isotropyrepresentation of $M$ splits into two inequivalent irreducible summands.Immediate and potential applications include new existence results for Ricciiterations.

The Prescribed Ricci Curvature Problem on Homogeneous Spaces with Intermediate Subgroups