| Project/Area Number |
20K03585
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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 | Kobe University |
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Principal Investigator |
Rossman W. F 神戸大学, 理学研究科, 教授 (50284485)
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| Co-Investigator(Kenkyū-buntansha) |
安本 真士 徳島大学, 大学院社会産業理工学研究部(理工学域), 講師 (70770543)
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Project Status |
Discontinued (Fiscal Year 2023)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2023: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2022: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | differential geometry / surface theory / transformation theory / surface representations / Lie sphere geometry / discrete surfaces / Moebius geometry / integrable systems / 離散的微分幾何学 / 離散曲面 / 離散曲線 / 特異点 / Darboux変換 / discretization / analysis |
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| Outline of Research at the Start |
本研究課題は，現代微分幾何の根幹をなす曲面の微分幾何学を，多角的なアプローチを用いて離散化し，離散化された曲面を解析する手法を確立することを目的とする．微分幾何的対象の離散化は，純粋数学だけでなく，CGや材料工学などの関連諸分野からも高い注目を集めている．一方，上記の研究分野を研究する際には，従来の数学研究をそのまま適用するだけでは不十分であり，これまでの微分幾何を，離散的な土台のもとで再整備・再構築することが求められている．
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| Outline of Final Research Achievements |
This research focused on the many structures that smooth surfaces have, and on maintaining this structure in the discrete analogues within surface theory. The following three issues were addressed: firstly, the study of how singularities appearing on surfaces are related to the properties of integrable systems of surfaces; secondly, the study of mathematical properties appearing in the construction of larger classes of discrete surfaces; thirdly, the study of smooth surfaces possibly having singularities and changes in their metric signature, by the methods of integrable systems.
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| Academic Significance and Societal Importance of the Research Achievements |
この研究の意義は、滑らかな曲面と離散曲面が持つ数学的構造のさらなる解明と理解の促進や、離散微分幾何学を研究するベルリン工科大学、ウィーン工科大学、イギリスのバース大学との連携を深めることにあります。
English translation: The significance is to further promote understanding of smooth and discrete surfaces, and to promote discrete differential geometry, and to deepen international collaboration.
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