2005 Fiscal Year Final Research Report Summary
Developments of nilpotent geometry and nilpotent analysis, and subriemannian geometry
| Project/Area Number |
16540065
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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 | Nara Women's University |
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Principal Investigator |
MORIMOTO Tohru Nara Women's University, Faculty of science, Professor, 理学部, 教授 (80025460)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIKAWA Goo Hokkaido Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (50176161)
FURUTANI Kenro Tokyo Science Univ., Faculty of Science and Technology, Professor, 理工学部, 教授 (70112901)
SATO Hajime Nagoya Univ., Graduate School of Polymathematics, Professor, 大学院・多元数理, 教授 (30011612)
AGAOKA Yoshio Hiroshima Univ., Faculty of Integrated Science, Professor, 総合科学部, 教授 (50192894)
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| Project Period (FY) |
2004 – 2005
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| Keywords | nilpotent geometry / nilpotent analysis / subriemannian geometry / Cartan connection / representation of Lie algebra and system of PDEs |
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| Research Abstract |
We developed nilpotent geometry and nilpotent analysis and applied them to subriemannian geometry. In particular, we have found a simple and general principle which associates systems of partial differential equations to representations of Lie algebras in the framework of nilpotent analysis.
We organized the following workshops and symposium :
1)Geometry in Nara on Quaternion structures, CR-structures and subriemannian structures, April 12-14,2004 at Nara WU.
2)Geometry in Nara around subriemannian geometries, December 13-15,2004 at Nara WU.
3)RIMS International symposium "Developments of Cartan geometry and related mathematical problems", October 24-27,2005, at RIMS Kyoto Univ
Among the invited from abroad were D.Alekssevsky, R.Bryant, P.Greiner, R.Montgomery, P.Nurowski, S.H.Wang, I.Zelenko, M.Zhitomirskii. We aimed to further develop nilpotent geometry and nilpotent analysis and to integrate related researches arising world-wide in various countries. The proceedings of the RIMS Symposium soon to appear contain many remarkable results obtained through the symposium.
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