The twistor space
Z
Z
of an oriented Riemannian
4
4
-manifold
M
M
admits a natural
1
1
-parameter family of Riemannian metrics
h
t
{h_t}
compatible with the almost-complex structures
J
1
{J_1}
and
J
2
{J_2}
introduced, respectively, by Atiyah, Hitchin and Singer, and Eells and Salamon. In the present note we describe the (real-analytic) manifolds
M
M
for which the Ricci tensor of
(
Z
,
h
t
)
\left ( {Z,{h_t}} \right )
is
J
n
{J_n}
-Hermitian,
n
=
1
or
2
n = 1\;{\text {or}}\;2
. This is used to supply examples giving a negative answer to the Blair and Ianus question of whether a compact almost-Kähler manifold with Hermitian Ricci tensor is Kählerian.