2021 Fiscal Year Research-status Report
| Project/Area Number |
15K04845
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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直川 耕祐 神戸大学, 理学研究科, 特別研究員(PD) (60740826) [Withdrawn]
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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| Keywords | 離散的微分幾何学 / 離散曲面 / 離散曲線 / 特異点 / Darboux変換 |
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| Outline of Annual Research Achievements |
This research is a study of how singular behavior of various types occurs within integrable systems related to surface geometry, with the following specific aims:
1) The notion of singular behavior has been broadened to include type-change behaviors and notions of completeness.
2) Transformation theory of surfaces and curves is playing an informative role in this research, in particular Darboux transformations have been frequently employed, along with the needed background Christoffel and Calapso transforms.
3) Discretization of curves and surfaces, along with singular behaviors in these cases, is being examined.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The following has been achieved:
1) After studying the singular behavior and type change behavior on particular surfaces existing in non-Riemannian spaceforms, the focus has shifted toward understanding various notions of completeness for such surfaces.
2) The final stages of joint work with J. Cho and T. Seno on discrete and semi-discrete mKdV equations from the viewpoint of variations of curves has been accomplished.
3) Work with S. Fujimori, Y. Kawakami, M. Kokubu, M. Umehara, K. Yamada, and S-D. Yang on completeness of geometric catenoids in non-Riemannian spaceforms has been finalized.
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| Strategy for Future Research Activity |
The following will be forthcoming:
1) With various notions of completeness for particular surfaces existing in non-Riemannian spaceforms in place, there is presently joint work with S. Fujimori, Y. Kawakami, M. Kokubu, M. Umehara, K. Yamada, and S-D. Yang on applications of those notions.
2) Progress has also been made on the completeness of a different class of analytically-represented catenoids, different from geometric catenoids, in joint work with S. Fujimori, Y. Kawakami, M. Kokubu, M. Umehara, K. Yamada, and S-D. Yang.
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| Causes of Carryover |
新型コロナウイルスの影響で予定していた外国と国内旅費が使えなくなった。次年度の旅費に利用する予定です。
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Research Products
(15 results)
