Complete Riemannian manifolds with pointwise pinched curvature
- Cite this article as:
- Chen, B. & Zhu, X. Invent. math. (2000) 140: 423. doi:10.1007/s002220000061
An analogous Bonnet-Myers theorem is obtained for a complete and positively curved n-dimensional (n≥3) Riemannian manifold Mn. We prove that if n≥4 and the curvature operator of Mn is pointwise pinched, or if n=3 and the Ricci curvature of M3 is pointwise pinched, then Mn is compact.