Group actions on symplectic manifolds and their quantization
| Project/Area Number |
23540072
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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 | Meiji University (2013-2016)
The University of Tokyo (2011-2012) |
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Principal Investigator |
Hiroshi Konno 明治大学, 理工学部, 専任教授 (20254138)
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| Project Period (FY) |
2011-04-28 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | moment map / geometric quantization / mean curvature flow / 平均曲率流 / ラグランジュ部分多様体 / モーメント写像 / リッチ平坦多様体 / 微分幾何学 / シンプレクティック幾何学 / シンプレクティック幾何 |
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| Outline of Final Research Achievements |
A moment map is defined when a Lie group acts on a symplectic manifold with certain conditions. In this project, we gave new applications of the geometry of moment maps. Firstly, we studied geometric quantization to clarify a mathematical reason for the polarization-independent principles in physics. In particular, we described the relation among Kahler polarizations and real polarizations on flag manifolds. Secondly, we construct various concrete examples of Lagrangian mean curvature flows in Calabi-Yau manifolds. We also described the structure of the singularities of these flows.
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Report
(7 results)
Research Products
(16 results)
