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.
Original language | English (US) |
---|---|
Pages (from-to) | 179-195 |
Number of pages | 17 |
Journal | Commentarii Mathematici Helvetici |
Volume | 56 |
Issue number | 1 |
DOIs | |
State | Published - Dec 1981 |
ASJC Scopus subject areas
- General Mathematics