  We show that the small quantum product of the generalized flag manifold $G/B$
is a product operation on $H^*(G/B)\otimes \bR[q_1,..., q_l]$ uniquely
determined by the fact that it is a deformation of the cup product on
$H^*(G/B)$, it is commutative, associative, graded with respect to
$\deg(q_i)=4$, it satisfies a certain relation (of degree two), and the
corresponding Dubrovin connection is flat. We deduce that it is again the
flatness of the Dubrovin connection which characterizes essentially the
solutions of the "quantum Giambelli problem" for $G/B$. This result gives new
proofs of the quantum Chevalley formula (proved by Peterson and
Fulton-Woodward), and of Fomin, Gelfand and Postnikov's description of the
quantization map for $Fl_n$.
