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2014 Fiscal Year Final Research Report

Geometries of spaces on which Spinor groups act.

Research Project

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Project/Area Number 24540101
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionMeijo University

Principal Investigator

HASHIMOTO Hideya  名城大学, 理工学部, 教授 (60218419)

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)
Research Collaborator OHASHI Misa  
Project Period (FY) 2012-04-01 – 2015-03-31
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
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.

Free Research Field

微分幾何学

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Published: 2016-06-03  

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