| C∞ Compactness for a Class of Riemannian Manifolds with Parallel Ricci Curvature |
| Received:May 29, 1998 |
| Key Words:
sectional curvature Ricci curvature injectivity radius diameter volume Jacobi field.
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| Fund Project:Supported by National Natural Science Foundation of China (19971081) |
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| Abstract: |
| In this paper we prove that the set of Riemannian manifolds with parallel Ricci curvature, lower bounds for sectional curvature and injectivity radius and a upper bound for volume is c∞ compact in Gromov-Hausdroff topology. As an application we also prove a pinching result which states that a Ricci flat manifold is flat under certain conditions. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2001.02.002 |
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