Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature
Let Mn,g,f be a complete gradient shrinking Ricci soliton of dimension n≥3. In this paper, we study the rigidity of Mn,g,f with pointwise pinching curvature and obtain some rigidity results. In particular, we prove that every n-dimensional gradient shrinking Ricci soliton Mn,g,f is isometric to ℝn o...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/4907963 |
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| Summary: | Let Mn,g,f be a complete gradient shrinking Ricci soliton of dimension n≥3. In this paper, we study the rigidity of Mn,g,f with pointwise pinching curvature and obtain some rigidity results. In particular, we prove that every n-dimensional gradient shrinking Ricci soliton Mn,g,f is isometric to ℝn or a finite quotient of Sn under some pointwise pinching curvature condition. The arguments mainly rely on algebraic curvature estimates and several analysis tools on Mn,g,f, such as the property of f-parabolic and a Liouville type theorem. |
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| ISSN: | 1687-9120 1687-9139 |