Let $X$ be complex manifold, let $h$ be a smooth hermitian metric on $\omega_{X}$ and $\Omega$ a Kähler form such that $\Omega^{n}=v(h)$. The Ricci curvature divided by $2\pi$ of $\Omega$ is the Chern-Weil form $-c_{1}(K_{X},h)$.