Abstract.
An analogous Bonnet-Myers theorem is obtained for a complete and positively curved n-dimensional (n≥3) Riemannian manifold M n. We prove that if n≥4 and the curvature operator of M n is pointwise pinched, or if n=3 and the Ricci curvature of M 3 is pointwise pinched, then M n is compact.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Oblatum 4-II-1999 & 10-XI-1999¶Published online: 21 February 2000
Rights and permissions
About this article
Cite this article
Chen, BL., Zhu, XP. Complete Riemannian manifolds with pointwise pinched curvature. Invent. math. 140, 423–452 (2000). https://doi.org/10.1007/s002220000061
Issue Date:
DOI: https://doi.org/10.1007/s002220000061