A geometric characterization of discrete Guichard nets and their transformations in integrable geometry
| Project/Area Number |
17F17734
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| Research Category |
Grant-in-Aid for JSPS Fellows
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| Allocation Type | Single-year Grants |
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| Section | 外国 |
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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) |
SZEWIECZEK GUDRUN 神戸大学, 理学研究科, 外国人特別研究員
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| Project Period (FY) |
2017-11-10 – 2019-03-31
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| Project Status |
Discontinued (Fiscal Year 2018)
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| Budget Amount *help |
¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2018: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 2017: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | channel surfaces / Guichard nets / R-congruences / discrete surfaces |
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| Outline of Annual Research Achievements |
Gudrun worked on the following projects:
1) The study of discrete channel surfaces, as joint work with myself and Gudrun's former Ph.D. advisor Udo Hertrich-Jeromin at the Technical University of Vienna. Following clues from the theory of smooth channel surfaces, which can be thought of as tubes with varying radius as one moves along a non-circular direction of the surface, Gudrun established why one particular way of discretizing is the best choice. Gudrun further examined possible applications, finding a characterization of discrete isothermic channel surfaces, and finding connections with multi-circular discrete nets. This work has been submitted for publication.
2) The study of discrete Guichard triply orthogonal systems, joint work with Joseph Cho at Kobe University and myself. In particular, Gudrun made the interesting discovery that the conformal diagonal surfaces of Guichard triply orthogonal systems can be minimal surfaces.
3) The study of Combescure and Ribaucour transformations of Guichard nets, as an extension of her Ph.D. thesis.
4) The study of discrete R-congruences, work that Gudrun is conducting with Thilo Roerig of the Technical University of Berlin.
All four projects described above were successful and are of interest to other researchers in Gudrun's field.
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| Research Progress Status |
平成30年度が最終年度であるため、記入しない。
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| Strategy for Future Research Activity |
平成30年度が最終年度であるため、記入しない。
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Report
(2 results)
Research Products
(8 results)
