Let (M,g,J) be a Kaehler manifold with riemannian curvature R viewed as a symmetric endomorphism of the 2-forms Λ2(TM). If ω is the symplectic form, I define the Riemann-Kaehler-Einstein equations:
R(ω)=λω
ω is a proper vector of the endomorphism R.
Have we a correspondence of the Riemann-Kaehler-Einstein equations with the Kaehler-Einstein equations?