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 $\Omega_{h_{\epsilon}}$ of the Chern connection on $L$ (with respect to $h_{\epsilon}$) can have an arbitrary negative part.

In order to define the *nef line bundles* on **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.