Study on geometry of symmetric R-spaces and their submanifolds
| Project/Area Number |
15K04855
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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 | Tokyo University of Science |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
TASAKI Hiroyuki 筑波大学, 数理物質系, 准教授 (30179684)
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| Research Collaborator |
Eschenburg Jost-Hinrich
Quast Peter
Kimura Taro
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 対称R空間 / 部分多様体 / 対蹠集合 / 外的対称空間 / リー群 / 対称空間 / 国際研究者交流 / ドイツ / 2-number |
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| Outline of Final Research Achievements |
In collaboration with Jost-Hinrich Eschenburg, we introduced the notion of an extrinsic symmetric subspace of an extrinsic symmetric space and gave a characterisation of extrinsic symmetric subspaces by using Lie triple systems.
In collaboration with Hiroyuki Tasaki, we classified maximal antipodal subgroups of the quotient groups of compact classical Lie groups and determined their great antipodal subgroups and by using them we classified maximal antipodal subgroups of the automorphism groups of compact classical Lie algebras.
In collaboration with Hiroyuki Tasaki and Osami Yasukura we classified maximal antipodal subgroups of compact exceptional Lie group G_2 and classified maximal antipodal sets of compact exceptional symmetric space G_2/SO(4). We gave an explicit description of them by using the realization of G_2 as the automorphism group of the Cayley algebra.
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Report
(4 results)
Research Products
(43 results)
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[Presentation] 実形の交叉2017
Author(s)
田崎博之
Organizer
第24回沼津研究会
Place of Presentation
沼津工業高等専門学校(静岡県・沼津市）
Year and Date
2017-03-06
Related Report
Invited
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[Presentation] 対蹠集合と実形の交叉2016
Author(s)
田崎博之
Organizer
第11回代数・解析・幾何学セミナー
Place of Presentation
鹿児島大学理学部（鹿児島県鹿児島市）
Year and Date
2016-02-16
Related Report
Invited
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