2022 Fiscal Year Final Research Report
Construction of discrete curves and discrete surfaces
| Project/Area Number |
19K03507
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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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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | Kurume Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | 離散Kirchhoff弾性棒 / 離散弾性曲線 / 離散単振り子方程式 / 共形平坦超曲面 |
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| Outline of Final Research Achievements |
From the viewpoint of discrete integrable geometry, we derived an explicit formula for the discrete Kirchhoff elastic rods in 3-dimensional Euclidean space. From the viewpoint of integrable geometry, we constructed an example of the curvature surfaces in generic conformally flat hypersurfaces in 4-dimensional Euclidean space and investigated its global behaviour.
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| Free Research Field |
差分幾何
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| Academic Significance and Societal Importance of the Research Achievements |
コンピュータグラフィクス分野ではしばしば一次元弾性体の数値シミュレーションが行われるが、本研究で求めた離散キルヒホフ弾性棒の明示公式は、そのような数値実験の理論的基盤としての役割を果たしうる。
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