# The hermitian Einstein manifolds

I take an hermitian manifold $(M,g,J)$ and I define from the riemannian curvature $R(X,Y)$ as a $2$-form: $$Ricc(J)= \sum_i R(J e_i,e_i)$$ with $(e_i)$ an orthonormal basis of the tangent. $$2R(J)=J Ricc(J)+ Ricc(J)J$$ $$r(J)=tr(R(J))$$ The hermitian Einstein metric verifies: $$R(J)_{ij}- \frac{1}{2} r(J)g_{ij}=0$$ Have you references about such a metric?