= Hodge star of the fundamental Hermitian form
{c}
{title2=$*\omega=\omega^{n-1}/(n-1)!$}
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.
Back to article page
