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.
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Oblatum 4-II-1999 & 10-XI-1999¶Published online: 21 February 2000
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Chen, BL., Zhu, XP. Complete Riemannian manifolds with pointwise pinched curvature. Invent. math. 140, 423–452 (2000). https://doi.org/10.1007/s002220000061
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DOI: https://doi.org/10.1007/s002220000061