Hodge star on middle-degree differential forms is conformally invariant
= Hodge star on middle-degree differential forms is conformally invariant
If a metric in dimension $n$ is rescaled by $\widetilde g=e^{2\omega}g$, then its Hodge star on $p$-forms satisfies $\widetilde *=e^{(n-2p)\omega}*$. The exponent vanishes for middle-degree forms with $n=2p$, so their self-dual and anti-self-dual subspaces depend only on the conformal class.