Hi.

If $f\rightarrow S$ is an open morphism with fibers of dimension n of reduced finite dimensionnal complex spaces (or universally open morphism with fibers of dimension n of locally noetherian, excellents and without embedded components or reduced schemes) it is true that

$f^{*}G$ torsion free for all torsion free coherent sheaf $G$ on $S$ $\Longrightarrow$ $f$ is flat ?

Thank you.