Hodge star of the fundamental Hermitian form ($\ast \omega ={\omega }^{n-1}/(n-1)!$)

In an adapted real orthonormal coframe, the fundamental form of a Hermitian manifold is $\omega ={\sum }_j{e}^j\wedge f^j$ and the Riemannian volume form is ${\omega }^n/n!$. The complex-linear Hodge star sends each summand to the product of all the other oriented two-dimensional factors. Summation gives the displayed formula, valid for every Hermitian manifold, without a Kähler assumption.