  Hartshorne in "Ample vector bundles" proved that $E$ is ample if and only if
$\OOO_{P(E)}(1)$ is ample. Here we generalize this result to flag manifolds
associated to a vector bundle $E$ on a complex manifold $X$: For a partition
$a$ we show that the line bundle $\it Q_a^s$ on the corresponding flag manifold
$\mathcal{F}l_s(E)$ is ample if and only if $ \SSS_aE $ is ample. In particular
$\det Q$ on $\it{G}_r(E)$ is ample if and only if $\wedge ^rE$ is ample.\\ We
give also a proof of the Ampleness Dominance theorem that does not depend on
the saturation property of the Littlewood-Richardson semigroup.
