Let $L$ be a line bundle over 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* over **complex analytic spaces**:

are there references about Hermitian metrics, differential forms, Chern connections in the

complex analytic spaceframework?

Any answer, comment, advice will be appreciated.

Thanks in advance.

Theory of Stein Spaces, and Gunning - RossiAnalytic Functions of Several Complex Variables. However, thank you for your advices. $\endgroup$ – Armando j18eos Mar 31 '17 at 8:04