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Integral pinching theorems

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Abstract:

Using Hamilton's Ricci flow we shall prove several pinching results for integral curvature. In particular, we show that if p>n/2$ and the L p norm of the curvature tensor is small and the diameter is bounded, then the manifold is an infra-nilmanifold. We also obtain a result on deforming metrics to positive sectional curvature.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Santa Barbara,¶CA 93106, USA. e-mail: dai@math.ucsb.edu; wei@math.ucsb.edu, USA

    X. Dai & G. Wei

  2. Department of Mathematics, University of California, Los Angeles, CA 90095, USA. e-mail: petersen@math.ucla.edu, USA

    P. Petersen

Authors
  1. X. Dai
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  2. P. Petersen
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  3. G. Wei
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Received: 17 February 1999

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Dai, X., Petersen, P. & Wei, G. Integral pinching theorems. manuscripta math. 101, 143–152 (2000). https://doi.org/10.1007/s002290050009

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  • DOI: https://doi.org/10.1007/s002290050009

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