2009 Fiscal Year Final Research Report
Characterization of homogeneous spaces admitting flat geometric structures by means of invariants
| Project/Area Number |
19540091
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Hiroshima University |
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Principal Investigator |
AGAOKA Yoshio Hiroshima University, 大学院・理学研究科, 教授 (50192894)
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| Co-Investigator(Kenkyū-buntansha) |
TAMARU Hiroshi 広島大学, 大学院・理学研究科, 准教授 (50306982)
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| Co-Investigator(Renkei-kenkyūsha) |
USAMI Hiroyuki 広島大学, 大学院・理学研究科, 准教授 (90192509)
NAKAYAMA Hiromichi 青山学院大学, 理工学部, 教授 (30227970)
KONNO Hitoshi 広島大学, 大学院・理学研究科, 准教授 (00291477)
KANEDA Eiji 大阪大学, 大学教育実践センター, 教授 (90116137)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 微分幾何 |
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| Research Abstract |
We study several conditions on homogeneous spaces (or Lie groups) in order that they admit flat geometric structures from the standpoint of invariant theory. In this research, we treat mainly projective and pseudo-Riemannian structures, and we succeed to obtain several necessary conditions to admit flat geometric structures for some cases. We also construct new homogeneous spaces admitting flat projective structures by using representation theory, and in addition, determine the existence or non-existence of almost flat pseudo-Riemannian structures on each 3-dimensional Lie group.
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Research Products
(25 results)
