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1 results

  • A round sphere theorem for positive sectional curvature

  • Changyu Xia
  • Journal:
    Compositio Mathematica / Volume 142 / Issue 5 / September 2006
    Published online by Cambridge University Press:
    25 September 2006, pp. 1327-1331
    Print publication:
    September 2006
    • Article
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  • Let $M$ be an $n$-dimensional complete connected Riemannian manifold with sectional curvature $\operatorname{sec}(M) \geq 1$ and radius $\operatorname{rad}(M)>\pi /2$. In this article, we show that if $\operatorname{conj}(M)$, the conjugate radius of $M$, is not less than $\operatorname{rad}(M)$, then $M$ is isometric to a round sphere of constant curvature.