  The Blaschke's conjecture asserts that if $\diam(M)=\text{Inj}(M)=\frac\pi2$
(up to a rescaling) for a complete Riemannian manifold $M$, then $M$ is
isometric to $\Bbb S^n(\frac12)$, ${\Bbb R\Bbb P}^{n}$, ${\Bbb C\Bbb P}^{n}$,
${\Bbb H\Bbb P}^{n}$ or ${\Bbb Ca\Bbb P}^{2}$ endowed with the canonical
metric. In the paper, we prove that the conjecture is true if we in addition
assume that $\sec_M\geq1$.
