Positive real (1, 1)-form
= Positive real (1, 1)-form
A real $(1,1)$-form $\varphi$ is positive when
$$
-i\varphi(\xi,\bar\xi)>0
$$
for every nonzero tangent vector $\xi$ of type $(1,0)$. Equivalently, the local Hermitian matrix in the representation $\varphi=i h_{j\bar k}dz^j\wedge d\bar z^k$ is positive definite.