2010 Fiscal Year Final Research Report
Geometric structure on geometric manifolds which admit Lie group transformations and various Rigidity
| Project/Area Number |
20340013
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Tokyo Metropolitan University |
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Principal Investigator |
KAMISHIMA Yoshinobu Tokyo Metropolitan University, 大学院・理工学研究科, 教授 (10125304)
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| Co-Investigator(Kenkyū-buntansha) |
MARTIN GUEST 首都大学東京, 大学院・理工学研究科, 教授 (10295470)
SOMA Teruhiko 首都大学東京, 大学院・理工学研究科, 教授 (50154688)
IMAI Jun 首都大学東京, 大学院・理工学研究科, 准教授 (70221132)
KAMIYA Shigeyasu 岡山理科大学, 工学部, 教授 (80122381)
HASEGAWA Keizo 新潟大学, 人文社会・教育系, 教授 (00208480)
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| Co-Investigator(Renkei-kenkyūsha) |
SAKAI Takashi 首都大学東京, 大学院・理工学研究科, 助教 (30381445)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 幾何学 / 微分幾何学 / 微分トポロジー |
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| Research Abstract |
We have examined the following projects.
(1) Approach from geometry and topology concerning conformally Fefferman-Lorentz manifolds.
(1) We proved the analogue of the Obata-Ferrand theorem to Lorentz manifolds.
(2) We proved the Kuiper's problem that if the developing map is not surjective on the universal cover of S^<n-1,1>, then it is a covering map onto its image under the existence of causal vector fields.
(2) We studied the infrasolv-fiber space structure and the smooth rigidity on the closed aspherical manifolds of the mixed type. As an application, we proved the smooth rigidity of compact aspherical homogeneous manifolds.
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