Differential geometric approach to discrete surfaces
| Project/Area Number |
15K04845
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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 | 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) |
直川 耕祐 神戸大学, 理学研究科, 特別研究員(PD) (60740826)
佐治 健太郎 神戸大学, 理学研究科, 教授 (70451432)
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| Project Period (FY) |
2015-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | differential geometry / surface theory / transformation theory / surface representations / Lie sphere geometry / discrete surfaces / Differential Geometry / Discrete Surface Theory / Lorentzian spaces / Omega surfaces / Darboux transformations / 離散的微分幾何学 / 離散曲面 / 離散曲線 / 特異点 / Darboux変換 / 半離散曲面 / discrete geometry / minimal surface / Omega surface / channel surfaces / orthogonal systems / Guichard surfaces / semi-discrete surfaces / integrable systems / Moebius geometry |
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| Outline of Final Research Achievements |
This was research on extending the rich mathematical structure of smooth surfaces to discretized surfaces, including studies of A) how singular behavior of various types on surfaces manifests itself within associated integrable systems, B) new methods of constructing discrete surfaces, and analysis of the properties that appear, C) smooth surfaces with integrable systems properties that can have singularities and/or signature type change.
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| Academic Significance and Societal Importance of the Research Achievements |
この研究の意義は離散曲面に関連する構造と性質の理解を深めることや、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いった離散曲面理論研究グループとの連携を深めることにあります。[English translation: This research creates expanded understanding of the structures of discrete surfaces, connecting with research groups at Berlin and Vienna Technical Universities, and Bath University.
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Report
(9 results)
Research Products
(85 results)
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[Journal Article] Analytic extension of Jorge-Meeks type maximal surfaces in Lorentz-Minkowski 3-space2017
Author(s)
Fujimori, S., Kawakami, Y., Kokubu, M., Rossman, W., Umehara, M. and Yamada, K.
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Journal Title
Osaka J. Math.
Volume: 54
Pages: 249-272
Related Report
Peer Reviewed / Int'l Joint Research
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