Deepening and merging twistor theory for indefinite or exceptional structure groups
| Project/Area Number |
16K05118
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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 | Fukushima University |
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Principal Investigator |
NAKATA Fuminori 福島大学, 人間発達文化学類, 准教授 (80467034)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | ツイスター理論 / 複素幾何学 / 位相幾何学 / 等質空間 / 微分幾何学 |
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| Outline of Final Research Achievements |
A double fibration concerning to the associative Grassmann manifold is studied via method of twistor theory, and its unknown geometric structure is studied. An explicit description of G2 Lie algebra is studied, and a new description of Hopf fibration is obtained as its application. Topological properties of homogeneous spaces with G2 symmetry is also studied. We succeeded to obtain an explicit description of geometric structures of such homogeneous spaces by making use of moving frame method. We also find that most of these homogeneous spaces are realized in terms of tautological vector bundle over the associative Grassmann manifold.
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| Academic Significance and Societal Importance of the Research Achievements |
ツイスター理論は数理物理学に端を発し，幾何学においても非常に大きな成果をもたらした実りある理論であるが，本研究ではその新たな可能性を開拓することに貢献がなされたと考える．具体的には，等質空間の構造や複数の等質空間の関係について，ツイスター理論の観点・発想による新しい結果を複数得たとともに，総合的な視点に基づく新たな研究課題の創出に至った．
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Report
(5 results)
Research Products
(11 results)
