Holomorphic fiber bundle with Stein base and Stein fibers

Abstract

In this article, we prove that if $\Pi :X\to \Omega$ is a surjective holomorphic map, with $\Omega$ a Stein space and $X$ a complex manifold of dimension $n\ge 3,$ and if, for every $x\in \Omega$ there exists an open neighborhood $U$ such that ${\Pi }^{-1}(U)$ is Stein, then $X$ is Stein