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 |
Section | 一般 |
Research Field |
Geometry
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Research Institution | Kumamoto University (2019-2020) Saga University (2015-2018) |
Principal Investigator |
Nakagawa Yasuhiro 熊本大学, 大学院先端科学研究部(理), 教授 (90250662)
|
Project Period (FY) |
2015-04-01 – 2021-03-31
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Project Status |
Completed (Fiscal Year 2020)
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Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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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 / Einstein・Kaehler 計量 / Kaehler・Ricci ソリトン / トーリック Fano 多様体 / 幾何学的不変式論 / Kaehlre・Ricci ソリトン |
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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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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Report
(7 results)
Research Products
(15 results)