| Project/Area Number |
18K03272
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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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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | Kanazawa University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
守屋 克洋 筑波大学, 数理物質系, 助教 (50322011)
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| Project Period (FY) |
2018-04-01 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2022: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
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| Keywords | 四元数多様体 / 超複素多様体 / 複素部分多様体 / c-射影構造 / supergravity c-map / rigid c-map / 錐的超複素多様体 / 運動量写像 / 部分多様体 |
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| Outline of Final Research Achievements |
We give a construction of a hypercomplex manifold from a quaternion manifold (Q/H-correspondence). We also find a construction of a quaternion manifold from a hypercomplex manifold (H/Q-correspondence). As a concrete example, we obtain a hypercomplex Hopf manifold, which does not allow any hyperkahler structures. In particular, as an application of H/Q-correspondence, it is possible to construct a quaternion manifold from a certain type of complex manifold, which follow from the fact that the tangent bundle of this complex manifold has the structure of a quaternion manifold.
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| Academic Significance and Societal Importance of the Research Achievements |
四元数多様体や超複素多様体は重要な研究対象であり，それらの構成は基本的なテーマである．本研究では，超複素運動量写像を用いて四元数多様体から超複素多様体を構成したが，超複素運動量写像の有用性を示したことや古典的な題材であるc-射影構造を活用して点でも学術的意義があると思われる．また，今後は物理学への応用もふまえ，更なる展開を考えていきたい．
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