Fundamental form of a Hermitian manifold
= Fundamental form of a Hermitian manifold
{title2=$\omega$}
For the underlying <Riemannian metric> $g$ and <complex structure> $J$, the fundamental form is $\omega(u,v)=g(Ju,v)$. It is a <real (1, 1)-form>. In complex dimension $n$, the compatible orientation has <Riemannian volume form> $\omega^n/n!$, and its <Hodge star operator> satisfies
$$
*\omega=\frac{\omega^{n-1}}{(n-1)!}.
$$