Topology of conformally flat Lorentz manifold and various geometric structures
| Project/Area Number |
24540087
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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 | Josai University (2014)
Tokyo Metropolitan University (2012-2013) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
長谷川 敬三 新潟大学, 人文社会・教育科学系, 教授 (00208480)
相馬 輝彦 首都大学東京, 理工学研究科, 教授 (50154688)
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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 |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 擬リーマン幾何学 / ローレンツ幾何学 / 微分トポロジー / Developing / Holonomy / Uniformization / 平坦 / Lorentz ｓtructure / Fefferman metric / Conformalｌｙ flat / Lightlike vector field / Weyl curvature / Bott tower / infranil manifold / complex contact / lcK structure / Lorentz structure / Seifert fibration / Complex contact / Infrasolv manifold / Holomorphic / Homogeneous |
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| Outline of Final Research Achievements |
When the curvature form for the Cartan connection of the parabolic geometry vanishes, a geomeric manifold has a flat structure. The Riemannian flat manifolds have been studied for a long time. In this note we study conformal Lorentz structure as a pseudo-Riemannian structure. If the Weyl conformal curvature tensor vanishes for a Lorentz manifold, it is called a conformally flat Lorentz manifold. We observed that its geometry and topology. We have shown the following results which never show up in Riemannian geometry. (1) If M is a compact complete Lorentzian similarity manifold, then M is a Lorentzian flat space form.
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Report
(4 results)
Research Products
(18 results)
