2003 Fiscal Year Final Research Report Summary
Geometric structures and differential equations on filtered manifolds
| Project/Area Number |
13640071
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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, Fac.of Sciences, Prof., 理学部, 教授 (80025460)
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| Co-Investigator(Kenkyū-buntansha) |
SATO Hajime Nagoya Univ., graduate sch.of Math., Prof., 多元数理, 教授 (30011612)
MACHIDA Yoshinori Numazu Tech.College, Asso.Prof., 助教授 (90141895)
ISHIKAWA Goo Hokkaido Univ., graduate sch.of Sci., Asso.Prof., 理学研究科, 助教授 (50176161)
KISO Kazuhiro Ehime Univ., Fac.of Sciences, Prof., 理学部, 教授 (60116928)
AGAOKA Yoshio Hiroshima Univ., Fac.of Int.Arts, Asso.Prof., 総合科学部, 助教授 (50192894)
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| Project Period (FY) |
2001 – 2003
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| Keywords | filtered manifold / nilpotent geometry / nilpotent analysis / subriemannian manifold / Cartan connection |
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| Research Abstract |
From the viewpoint of nilpotent geometry and analysis, we have been developing general theories on geometric, structures and differential equations on filtered manifolds. More recently, as applications of these theories, we have been carrying detailed studies on various concrete geometric structures. In particular, applying the general theory of Morimoto to subriemannian geometry, we have obtained the following remarkable theorem : There exists a canonical Cartan connection associated with a subriemannian manifold satisfying Hormander condition and having constant first order approximation.
We have also determined, up to quotient by discrete groups, the homogeneous subriemannian contact manifolds whose automorphism groups are of maximal dimension. The automorphism groups are also classified into three isomorphic classes.
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