Real (p, p)-form
= Real (p, p)-form
{title2=$\overline\eta=\eta$}
A <differential form of type (p, q)> with equal holomorphic and antiholomorphic degrees is real when it is fixed by <complex conjugation>. For such a form, $\overline{\bar\partial\eta}=\partial\eta$, so $\bar\partial\eta=0$ implies $d\eta=0$. The converse follows from the distinct types of $\partial\eta$ and $\bar\partial\eta$.