LetM be a 3-dimensional quasi-Sasakian manifold. On such a manifold, the so-called structure function β is defined. With the help of this function, we find necessary and sufficient conditions forM to be conformally flat. Next it is proved that ifM is additionally conformally flat with β = const., then (a)M is locally a product ofR and a 2-dimensional Kählerian space of constant Gauss curvature (the cosymplectic case), or (b)M is of constant positive curvature (the non cosymplectic case; here the quasi-Sasakian structure is homothetic to a Sasakian structure). An example of a 3-dimensional quasi-Sasakian structure being conformally flat with nonconstant structure function is also described. For conformally flat quasi-Sasakian manifolds of higher dimensions see [O1]
At first, a necessary and sufficient condition for a Khler-Norden manifold to be holomorphic Einstein is found. Next, it
is shown that the so-called (real) generalized Einstein conditions for Khler-Norden manifolds are not essential since the
scalarcurvature of such manifolds is constant. In this context, we study generalized holomorphic Einstein conditions. Using
the one-to-one correspondence between Khler-Norden structures and holomorphic Riemannian metrics, we establish necessary
and sufficient conditions for Khler-Norden manifolds to satisfy the generalized holomorphic Einstein conditions. And a class
of new examples of such manifolds is presented. Finally, in virtue of the obtained results, we mention that Theorems 1 and
2 of H. Kim and J. Kim  are not true in general.