Inventiones mathematicae

, Volume 140, Issue 2, pp 423–452

Complete Riemannian manifolds with pointwise pinched curvature

Authors

  • Bing-Long Chen
    • Department of Mathematics, Zhongshan University, Guangzhou, P.R. China
  • Xi-Ping Zhu
    • Department of Mathematics, Zhongshan University, Guangzhou, P.R. China

DOI: 10.1007/s002220000061

Cite this article as:
Chen, B. & Zhu, X. Invent. math. (2000) 140: 423. doi:10.1007/s002220000061

Abstract.

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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© Springer-Verlag Berlin Heidelberg 2000