  In this paper, we consider the morphisms from projective spaces to flag
varieties. We show that the morphisms can only be constant under some special
conditions. As a consequence, we prove that the splitting types of unsplit
uniform $r$-bundles on $\mathbb{P}^m$ can not be
$(a_1,\dots,a_1,a_2,\dots,a_{r-k+1})$ for $1\le k\le m-2$.
