Let $L$ be a line bundle on a compact complex manifold $X$ with a Hermitian metric $\omega$: $L$ is said numerically effective (nef, for short) if for any $\epsilon>0$ there exists a smooth Hermitian metric $h_{\epsilon}$ on $L$ such that \begin{equation*} \Omega_{h_{\epsilon}}\geq-\epsilon\omega; \end{equation*} that is the curvature form of the Chern connection on $L$ (with respect to $h_{\epsilon}$) can have an arbitrary negative part.

In order to define the nef line bundle over complex analytic spaces:

are there references about Hermitian metrics, differential forms, Chern connections in the complex analytic space framework?

Any answer, comment, advice will be appreciated.

Thanks in advance.