A generalization of the Kaehler-Einstein metrics

Question

Let $(M,\omega)$ be a Kaehler manifold with Kaehler form $\omega$ and Ricci form $\rho$. I consider the following equation:

$$\omega -\rho =\partial \bar{\partial} log(r)$$

where $r$ is the scalar curvature. Is it a generalization of the Kaehler-Einstein metrics or does it follow that $\omega$ is a Kaehler-Einstein metric?