Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (1): 321-330.doi: 10.1016/S0252-9602(11)60232-4

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A DIFFERENTIABLE SPHERE THEOREM WITH PINCHING INTEGRAL RICCI CURVATURE

 WANG Pei-He, CHEN Chun-Li   

  1. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China;Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2009-08-31 Online:2011-01-20 Published:2011-01-20
  • Supported by:

    Supported by the NNSF of China (10671066) and the NSF of Shandong Province (Q2008A08), and Scientific Research Foundation of QFNU

Abstract:

In this article, we introduce the Hausdorff convergence to derive a differen-tiable sphere theorem which shows an interesting rigidity phenomenon on some kind of manifolds.

Key words: k-th Ricci curvature, Hausdorff convergence, differentiable sphere theorem, harmonic coordinate, integral Ricci curvature

CLC Number: 

  • 53C20
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