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A round sphere theorem for positive sectional curvature

Published online by Cambridge University Press:  25 September 2006

Changyu Xia
Changyu Xia
Affiliation:
Departamento de Matemática – IE, Universidade de Brasília, Campus Universitário, 70910-900 Brasília DF, Brazilxia@mat.unb.br
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Abstract

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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.

Keywords

rigiditypositively curved manifoldsconjugate radius53C20
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 5 , September 2006 , pp. 1327 - 1331
Copyright
Foundation Compositio Mathematica 2006