2020 Fiscal Year Final Research Report
Studies on Kobayashi-Hitchin correspondence from the view point of Kahelre-Ricci flow
| Project/Area Number |
15K04848
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kumamoto University (2019-2020)
Saga University (2015-2018) |
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Principal Investigator |
Nakagawa Yasuhiro 熊本大学, 大学院先端科学研究部(理), 教授 (90250662)
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| Project Period (FY) |
2015-04-01 – 2021-03-31
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| Keywords | Einstein・Kaehler計量 / Kaehler・Ricciソリトン / 満渕ソリトン / 安定性 / トーリックFano多様体 / KSM多様体 |
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| Outline of Final Research Achievements |
We introduced the notion of KSM-manifold, which has the structure of a fiber bundle over an Einstein-Kaehler Fano manifold whose fiber is a toric Fano manifold, and proved that every KSM-manifold admits a Kaehler-Ricci soliton. In particular, by choosing a non-homogeneous Einstein-Kaehler Fano manifold as a base-space, then we can obtain an example of non-almost-homogeneous Kaehler-Ricci soliton.
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| Free Research Field |
複素幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
Einstein・Kaehler計量やその一般化である定スカラー曲率Kaehler計量，端的Kaehler計量，Kaehler・Ricciソリトン等の知られている具体例は，大きな群が作用する概等質的なものがほとんどである．我々の考えたKSM多様体は底空間として勝手なEinstein・Kaehler・Fano多様体を考えることができるので，等質的でないEinstein・Kaehler・Fano多様体を底空間に選べば，概等質的でないKaehler・Ricciソリトンを多数構成できる．
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