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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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A sphere theorem for manifolds of positive Ricci curvature
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by Katsuhiro Shiohama PDF
Trans. Amer. Math. Soc. 275 (1983), 811-819 Request permission

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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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 275 (1983), 811-819
  • MSC: Primary 53C20
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0682734-1
  • MathSciNet review: 682734