| 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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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2003: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2002: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2001: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | filtered manifold / nilpotent geometry / nilpotent analysis / subriemannian manifold / Cartan connection / サブリーマン構造 / サブリーマン接触多様体 / モンジュ・アンペール方程式 / 幾何構造 / カルノ・カラテオドリー計量 |
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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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