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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A sphere theorem for manifolds of positive Ricci curvature


Author: Katsuhiro Shiohama
Journal: Trans. Amer. Math. Soc. 275 (1983), 811-819
MSC: Primary 53C20
MathSciNet review: 682734
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Abstract: Instead of injectivity radius, the contractibility radius is estimated for a class of complete manifolds such that $ {\text{Ri}}{{\text{c}}_M} \geqslant 1,{K_M} \geqslant - {\kappa ^2}$ and the volume of $ M \geqslant $ the volume of the $ (\pi - \varepsilon )$-ball on the unit $ m$-sphere, $ m = {\text{dim }}M$. Then for a suitable choice of $ \varepsilon = \varepsilon (m,k)$ every $ M$ belonging to this class is homeomorphic to $ {S^m}$.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0682734-1
Article copyright: © Copyright 1983 American Mathematical Society