2016 Fiscal Year Final Research Report
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
|
| Keywords | moment map / geometric quantization / mean curvature flow |
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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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| Free Research Field |
differential geometry
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