| Project/Area Number |
15540055
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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 | Hokkaido University of education |
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Principal Investigator |
YATSUI Tomoaki Hokkaido University of Education, Faculty of education, Asahikawa, Assistant Professor, 教育学部・旭川校, 助教授 (00261371)
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| Co-Investigator(Kenkyū-buntansha) |
FUKUI Masaki Hokkaido University of Education, Faculty of education, Asahikawa, Professor, 教育学部・旭川校, 教授 (20002628)
OKUYAMA Teturo Hokkaido University of Education, Faculty of education, Asahikawa, Professor, 教育学部・旭川校, 教授 (60128733)
ABE Osamu Hokkaido University of Education, Faculty of education, Asahikawa, Assistant Professor, 教育学部・旭川校, 助教授 (30202659)
KOMURO Naoto Hokkaido University of Education, Faculty of education, Asahikawa, Assistant Professor, 教育学部・旭川校, 助教授 (30195862)
KITAYAMA Masashi Hokkaido University of Education, Faculty of education, Kushiro, Professor, 教育学部・釧路校, 教授 (80169888)
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| Project Period (FY) |
2003 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2004: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2003: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | Cartan connecton / Invariants / diffferential equation |
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| Research Abstract |
In this project, we reserched the geometric invariants of the system of differential equtations of finite type. The system (Χ) of (k+1)-th order holonomic differential equations of integrable type defines an open submanifold R of k-jet space j^k and a differential system E on R. The symbol algebra of the pseudo-projective structure of order k+1 bidegree (m+1,1) of (R ; E,F) on R associated with (Χ) is a pseudo-projective fundamental graded Lie algebra of order k+1 of bidegree (n,r). N.Tanaka showed that there is naturally a normal Cartan connection (P,ω) of type G/G^<(0)> associated with E. Moreover the harmonic part HK of the curvature function K of (P,ω) generates the fundamental invariants of the Cartanconnection (P,ω), which takes values in the second generalized Spencer cohomology space H^2(δ). Therefore we need to investigate the space H^2(δ). We first obtained the non-vanishing subspaces of the generalized Spencer cohomology space H^2(δ) of pseudo-projective graded Lie algebras. B.Doubrov showed that the curvature function HK of the Cartan connection takes values in the subspace F^1H^2(δ) of H^2(δ). We otained the generators of subspaces F^1H^2(δ) in case δ is a pseudo-projectiv graded Lie algebra of order k+1 of bidegree (m+1,1).
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