Let $(X,h)$ be a Hermitian manifold of complex dimension $n$, and let $(U,z)$ be a holomorphic coordinate chart with $z=(z_1,\dots,z_n)$ and $z_j=x_j+i y_j$. Write the local covariant Hermitian metric tensor on $U$ as
so that $H=(h_{i\bar j})_{i,j=1}^n$ is a positive Hermitian matrix at each point of $U$. Suppose the Hermitian volume form $dV_h$ is normalized pointwise as follows: for every point $p\in X$ and every complex coframe $\alpha_1(p),\dots,\alpha_n(p)$ of $T_p^{*(1,0)}X$ satisfying