Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1983-0682734-1
MathSciNet review: 682734
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 ${S^m}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 53C20

Retrieve articles in all journals with MSC: 53C20


Additional Information

Article copyright: © Copyright 1983 American Mathematical Society