2012 Fiscal Year Final Research Report
Gauge theoretical approach to Einstein metrics and Ricci flow
| Project/Area Number |
20540090
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Sophia University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TSUZUKI Masao 上智大学, 理工学部, 准教授 (80296946)
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| Project Period (FY) |
2008 – 2012
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| Keywords | アインシュタイン計量 / リッチフロー |
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| Research Abstract |
We proved new obstructions to the existence of Einstein metricsand non-singular solutions to normalized Ricci flow on 4-manifolds by using Seiberg-Wittenmonopole equations. As some applications of these new obstructions to 4-dimensionalgeometry, we proved a new existence theorem of 4-manifolds without Einstein metrics. Wealso proved the existence of 4-manifolds which admit no Einstein metric, but satisfy theHitchin-Thorpe inequality with volume entropy term. Moreover, we were able to prove thatthere exist infinitely many 4-manifolds which cannot admit non-singular solutions tonormalized Ricci flow, but satisfy Hitchin-Thorpe type inequality.
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