  We study the properties of Ricci curvature of ${\mathfrak{g}}$-manifolds with
particular attention paid to higher dimensional abelian Lie algebra case. The
relations between Ricci curvature of the manifold and the Ricci curvature of
the transverse manifold of the characteristic foliation are investigated. In
particular, sufficient conditions are found under which the
${\mathfrak{g}}$-manifold can be a Ricci soliton or a gradient Ricci soliton.
Finally, we obtain a amazing (non-existence) higher dimensional generalization
of the Boyer-Galicki theorem on Einstein K-manifolds for a special class of
abelian ${\mathfrak{g}}$-manifolds.
