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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On the fundamental groups of manifolds with almost-nonnegative Ricci curvature

Author: Guofang Wei
Journal: Proc. Amer. Math. Soc. 110 (1990), 197-199
MSC: Primary 53C20; Secondary 20F34, 22E40, 57M05, 57S20
MathSciNet review: 1021214
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Abstract | References | Similar Articles | Additional Information

Abstract: We give an upper bound on the growth of $ {\pi _1}\left( M \right)$ for a class of manifolds $ M$ with Ricci curvature $ {\text{Ri}}{{\text{c}}_M} \geq - \varepsilon $, diameter $ d\left( M \right) = 1$, and volume $ {\text{vol}}\left( M \right) \geq \upsilon $.

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

  • [1] Michael T. Anderson, Short geodesics and gravitational instantons, J. Differential Geom. 31 (1990), no. 1, 265–275. MR 1030673 (91b:53040)
  • [2] M. Gromov, Synthetic geometry in Riemannian manifolds, Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fennica, Helsinki, 1980, pp. 415–419. MR 562635 (81g:53029)
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  • [4] J. Milnor, A note on curvature and fundamental group, J. Differential Geometry 2 (1968), 1–7. MR 0232311 (38 #636)

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Additional Information

PII: S 0002-9939(1990)1021214-X
Article copyright: © Copyright 1990 American Mathematical Society

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