| Project/Area Number |
17K05232
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Yokkaichi University |
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Principal Investigator |
Morimoto Tohru 四日市大学, 関孝和数学研究所, 研究員 (80025460)
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 幾何構造の同値問題 / 外在的幾何 / 内在的幾何 / 包合的な微分方程式系 / 不変量 / 幾何構造の同地問題 / 包合的な線形微分方程式系 / 巾霊幾何 / 外在的幾何の同値問題 / 内在的幾何の同値問題 / サブリーマン幾何 / 微分方程式の幾何 / 幾何構造の延長理論 / 旗多様体 / 幾何構造の不変量 / filtered manifold / extrinsic geometry / flag variety / involutive PDEs / equivalence problem / invariant / simple Lie algebras / 巾零幾何 / 巾零解析 / 外在的幾何の不変量 / 線形微分方程式系の不変量 / 幾何構造 / 微分方程式系 / Lie-Klein-Cartan |
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| Outline of Final Research Achievements |
We, joint with Boris Doubrov and Yoshinori Machida, have established a unified general theory of extrinsic geometry and linear differential equations on a basis of nilpotent geometry and nilpotent analysis, and published a paper entitled:
Extrinsic geometry and linear differential equations, in Sigma. As an application of the general theory, we then have carried out detailed studies on extrinsic geometry and linear differential equations of sl(3)type and have classified all the transitive geometric structures.
We joint with Jaehyun Hong, have established a unified general theory of intrinsic geometry by integrating and improving the previous works, and put a preprint : Prolongations, invariants, and fundamental identities, in ArXiv math.In particular we have given a general algorithm to find a fundamental system of invariant of an arbitrary G-structure( in an extended sense)on a filtered manifold. We are then applying the above theory to complex geometry and subRiemannian geometry.
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| Academic Significance and Societal Importance of the Research Achievements |
幾何には外在的幾何と内在的幾何の区別がある。
先に述べた、外在的幾何における統一理論と内在的幾何における統一理論は、その双方が互いに連携し、古典微分幾何の基本原理を与えるものであり、幾何における深い理解と広い応用をもたらすものであると思われる。
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