  Let $G$ be a compact connected Lie group and $H$ a closed subgroup of $G$.
Suppose the homogeneous space $G/H$ is effective and has dimension 3 or higher.
Consider a $G$-invariant, symmetric, positive-semidefinite, nonzero
(0,2)-tensor field $T$ on $G/H$. Assume that $H$ is a maximal connected Lie
subgroup of $G$. We prove the existence of a $G$-invariant Riemannian metric
$g$ and a positive number $c$ such that the Ricci curvature of $g$ coincides
with $cT$ on $G/H$. Afterwards, we examine what happens when the maximality
hypothesis fails to hold.
