On the fundamental groups of manifolds with almost-nonnegative Ricci curvature
HTML articles powered by AMS MathViewer
- by Guofang Wei
- Proc. Amer. Math. Soc. 110 (1990), 197-199
- DOI: https://doi.org/10.1090/S0002-9939-1990-1021214-X
- PDF | Request permission
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
- Michael T. Anderson, Short geodesics and gravitational instantons, J. Differential Geom. 31 (1990), no. 1, 265–275. MR 1030673
- 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 —, Structures métriques pour les variétés Riemanniennes, Cedic Fernand-Nathan, Paris, 1981.
- J. Milnor, A note on curvature and fundamental group, J. Differential Geometry 2 (1968), 1–7. MR 232311
Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 197-199
- MSC: Primary 53C20; Secondary 20F34, 22E40, 57M05, 57S20
- DOI: https://doi.org/10.1090/S0002-9939-1990-1021214-X
- MathSciNet review: 1021214