#### Vol. 282, No. 2, 2016

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On Blaschke's conjecture

### Xiaole Su, Hongwei Sun and Yusheng Wang

Vol. 282 (2016), No. 2, 479–485
##### Abstract

Blaschke’s conjecture asserts that if a complete Riemannian manifold $M$ satisfies $diam\left(M\right)=Inj\left(M\right)=\frac{\pi }{2}$, then $M$ is isometric to ${\mathbb{S}}^{n}\left(\frac{1}{2}\right)$ or to the real, complex, quaternionic or octonionic projective plane with its canonical metric. We prove that the conjecture is true under the assumption that ${sec}_{M}\ge 1$.

##### Keywords
Blaschke's conjecture, Berger's rigidity theorem, Toponogov's comparison theorem
Primary: 53C20