Title: The Prescribed Ricci Curvature Problem on Homogeneous Spaces with Intermediate Subgroups,
Abstract: 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 homogeneous
space $M=G/H$. We obtain a sufficient condition for the existence of
$g\in\mathcal M$ and $c>0$ such that the Ricci curvature of $g$ equals $cT$ for
a given $T\in\mathcal M$. This condition is also necessary if the isotropy
representation of $M$ splits into two inequivalent irreducible summands.
Immediate and potential applications include new existence results for Ricci
iterations.