Fano manifolds whose elementary contractions are smooth $\mathbb   P^1$-fibrations: A geometric characterization of flag varieties
  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 $G$. 
Gianluca Occhetta, Luis E. Sol\'a Conde, Kiwamu Watanabe, and   Jaros{\l}aw A. Wi\'sniewski
math.AG