| Project/Area Number |
24540101
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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 | Meijo University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
EJIRI Norio 名城大学, 理工学部, 教授 (80145656)
MASHIMO Katsuya 法政大学, 理工学部, 教授 (50157187)
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| Research Collaborator |
OHASHI Misa
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2013: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | ケーリー代数 / 例外型単純リー群G２ / スピノール群 / グラスマン幾何学 / Stiefel多様体 / fibre bundle structure / Maurer Cartan form / Moduli 空間 / 例外群 / 合同類 / ホロノミー群 / 等経超曲面 / 不変部分多様体 / クリフォード群 / spinor群 / 概複素構造 / Grassmann多様体 / 幾何構造 / Clifford algebra / 例外型単純リー群G2 / Spin(7) / グラスマン多様体 / 自己同型群 / 変形理論 |
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| Outline of Final Research Achievements |
We investigate the real Stiefel manifolds Vk(Rn) = SO(n)/SO(n－ k) for n=7 or n=8. If we identify R7 and R8 with purely imaginary octonions and octonions, respectively, then some real Stiefel manifolds can be represented as V2(R7) = G2/SU(2), V2(R8) = Spin(7)/SU(3), and V3(R8) = Spin(7)/SU(2). Therefore each real Stiefel manifold of this type can be represented as an orbit of the action of the Lie group G2 or Spin(7). In our study, we give the orbit decompositions of the other Stiefel manifolds related to the octonions under the action of Lie group G2 and Spin(7). Then we obtain new fibre bundle structures of some real Stiefel manifolds. From these facts, we obtain the difference between the SO(n)-geometries and G2, Spin(7)-geometries.
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