| Gap Theorem on Complete Noncompact Riemannian Manifold |
| Received:March 26, 2009 Revised:July 03, 2009 |
| Key Words:
Ricci curvature conformally flat gap theorem.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.70631003), the Natural Science Foundation of Anhui Education Department (Grant No.KJ2011A061), the Natural Science Foundation of Anhui Science and Technology Department (Grant No.1104606M01) and the Doctor of Philosophy Foundation of Anhui University of Architecture (Grant No.2007-6-3). |
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| Abstract: |
| A gap theorem on complete noncompact $n$-dimensional locally conformally flat Riemannian manifold with nonnegative and bounded Ricci curvature is proved. If there holds the following condition: $$\int_{0}^{r}sk(x_{0},s)\d s=o(\log r)$$ then the manifold is flat. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.03.006 |
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