The Riemann-Kaehler-Einstein equations

Question

Let $(M,g,J)$ be a Kaehler manifold with riemannian curvature $R$ viewed as a symmetric endomorphism of the 2-forms $\Lambda^2(TM)$. If $\omega$ is the symplectic form, I define the Riemann-Kaehler-Einstein equations:

$$R(\omega)=\lambda \omega$$

$\omega$ is a proper vector of the endomorphism $R$.

Have we a correspondence of the Riemann-Kaehler-Einstein equations with the Kaehler-Einstein equations?