2014 Fiscal Year Final Research Report
Geometries of spaces on which Spinor groups act.
| 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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| 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 |
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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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| Free Research Field |
微分幾何学
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