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A round sphere theorem for positive sectional curvature
Published online by Cambridge University Press: 25 September 2006
Abstract
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.
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- Research Article
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- Foundation Compositio Mathematica 2006
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