Curvature, diameter and betti numbers
- 1 December 1981
- journal article
- Published by European Mathematical Society - EMS - Publishing House GmbH in Commentarii Mathematici Helvetici
- Vol. 56 (1) , 179-195
- https://doi.org/10.1007/bf02566208
Abstract
We give an upper bound for the Betti numbers of a compact Riemannian manifold in terms of its diameter and the lower bound of the sectional curvatures. This estimate in particular shows that most manifolds admit no metrics of non-negative sectional curvature.Keywords
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