Generalized Einstein conditions on holomorphic Riemannian manifolds (Q879214)

First the authors give a necessary and sufficient condition for a Kähler--Norden manifold to be holomorphic Einstein. They show that that some generalized Einstein conditions for Kähler--Norden manifolds imply that the scalar curvature is constant. This motivates to consider their holomorphic versions. Using the one-to-one correspondence between Kähler--Norden structures and holomorphic Riemannian metrics, the authors find characterizations of these generalized holomorphic Einstein conditions. Finally some examples are presented.