2009 Fiscal Year Final Research Report
Developments of nilpotent geometry and nilpotent analysis
| Project/Area Number |
19540082
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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 | Kyoto University (2008-2009)
Nara Women's University (2007) |
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Principal Investigator |
MORIMOTO Tohru Kyoto University, 数理解析研究所, 長期研究員 (80025460)
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| Co-Investigator(Kenkyū-buntansha) |
KOISO Miyuki 奈良女子大学, 理学部, 教授 (10178189)
ARAKAWA Tomoyuki 奈良女子大学, 理学部, 准教授 (40377974)
ISHIKAWA Goo 北海道大学, 大学院・理学研究科, 教授 (50176161)
FURUTANI Kenro 東京理科大学, 理工学部, 教授 (70112901)
MACHIDA Yoshinori 沼津工業高等専門学校, 教養科, 准教授 (90141895)
KIYOHARA Kazuyoshi 岡山大学, 自然科学研究科, 教授 (80153245)
AGAOKA Yoshio 広島大学, 総合科学部, 教授 (50192894)
KISO Kazuhiro 愛媛大学, 名誉教授 (60116928)
NAKANISHI Nobutada 岐阜経済大, 経営学部, 教授 (50124053)
KATAGIRI Minyo 京都大学, 奈良女子理学部, 准教授 (60263422)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 巾零幾何 / 巾零解析 / フィルター付き多様体 / リー環の表現と微分方程式 / 旗多様体での外在的幾何 / 線形偏微分方程式系の不変量 |
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| Research Abstract |
Based on nilpotent geometry and analysis, a trinity of representation of Lie algebras, integrable system of linear differential equations and extrinsic geometry in flag manifolds is established. Moreover, we obtain a general method to calculate the invariants of an integrable system of linear differential equations (or those of a submanifold in a flag manifold) associated with a representation of a Lie algebra, if the Lie algebra is simple.
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