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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| Format: | Article |
| Language: | English |
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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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| author | Yawei Chu Dehe Li Jundong Zhou |
| author_facet | Yawei Chu Dehe Li Jundong Zhou |
| author_sort | Yawei Chu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f980ad348b6e43da901c2c53f2b86d80 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-f980ad348b6e43da901c2c53f2b86d802025-02-03T01:24:59ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/49079634907963Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian CurvatureYawei Chu0Dehe Li1Jundong Zhou2School of Mathematics and Statistics, Fuyang Normal University, Fuyang, Anhui 236037, ChinaSchool of Mathematics and Statistics, Anyang Normal University, Anyang, Henan 455000, ChinaSchool of Mathematics and Statistics, Fuyang Normal University, Fuyang, Anhui 236037, ChinaLet 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.http://dx.doi.org/10.1155/2021/4907963 |
| spellingShingle | Yawei Chu Dehe Li Jundong Zhou Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature Advances in Mathematical Physics |
| title | Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature |
| title_full | Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature |
| title_fullStr | Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature |
| title_full_unstemmed | Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature |
| title_short | Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature |
| title_sort | rigidity of complete gradient shrinkers with pointwise pinching riemannian curvature |
| url | http://dx.doi.org/10.1155/2021/4907963 |
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