Complete gradient shrinking Ricci solitons have finite topological type |
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Institution: | 1. Department of Mathematics, Capital Normal University, Beijing, PR China;2. Chern Institute of Mathematics, Weijin Road 94, Tianjin 300071, PR China |
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Abstract: | We show that a complete Riemannian manifold has finite topological type (i.e., homeomorphic to the interior of a compact manifold with boundary), provided its Bakry–Émery Ricci tensor has a positive lower bound, and either of the following conditions:(i) the Ricci curvature is bounded from above;(ii) the Ricci curvature is bounded from below and injectivity radius is bounded away from zero.Moreover, a complete shrinking Ricci soliton has finite topological type if its scalar curvature is bounded. To cite this article: F.-q. Fang et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008). |
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