  The present paper provides a geometric characterization of complete flag
varieties for semisimple algebraic groups. Namely, if $X$ is a Fano manifold
whose all elementary contractions are $\mathbb P^1$-fibrations then $X$ is
isomorphic to the complete flag manifold $G/B$ where $G$ is a semi-simple Lie
algebraic group and $B$ is a Borel subgroup of $G$.
