Complete Riemannian manifolds with pointwise pinched curvature
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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.
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