Real (1, 1)-form
= Real (1, 1)-form
A <differential form of type (p, q)> $\varphi$ of type $(1,1)$ is real when $\bar\varphi=\varphi$. Locally this is equivalent to
$$
\varphi=i\sum_{j,k}h_{j\bar k}\,dz^j\wedge d\bar z^k
$$
for a Hermitian matrix $(h_{j\bar k})$.