2018 Fiscal Year Final Research Report
Construction of CMC tori by infinite times Bianchi-Baecklund transformations
| Project/Area Number |
17H07321
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Okinawa National College of Technology |
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Principal Investigator |
Ogata Yuta 沖縄工業高等専門学校, 総合科学科, 講師 (50800801)
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| Research Collaborator |
Cho Joseph
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| Project Period (FY) |
2017-08-25 – 2019-03-31
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| Keywords | 平均曲率一定曲面 / 変換理論 / 可積分系 |
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| Outline of Final Research Achievements |
(1) We have defined a special Bianchi-Baecklund transformation via loop group methods and constructed new examples of CMC surfaces. We have also shown a method to construct positon-like solutions which have some different properties from the famous soliton solutions for the sinh-Gordon equation.
(2) We have proved the equivalence between the classical Bianchi-Baecklund transformations and simple factor dressings directly, using a different method from previous studies. As a result, we have shown the relationship between parameters of positon-like solutions for the sinh-Gordon equation and the extended fames for positon-like CMC surfaces.
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| Free Research Field |
微分幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究に用いている「Bianchi-Baecklund変換」は、幾何学的側面だけでなく、可積分系理論においても有名な変換であり、「ソリトン解」と呼ばれるsinh-Gordon方程式の解を与えることが既に知られている。本研究により、「ポジトン型解」と呼ばれるsinh-Gordon方程式の別の重要な解を構成し、その解析を行った。本研究は、幾何学的に興味深い曲面の構成理論を研究しているだけでなく、可積分系理論の応用例という点で学術的貢献を与えるものである。
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