2017 Fiscal Year Final Research Report
Symmetry of crystals and geometry of minimal surfaces
| Project/Area Number |
25400072
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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 | Nara Women's University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
堂寺 知成 近畿大学, 理工学部, 教授 (30217616)
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Keywords | 極小曲面 / ジャイロイド曲面 / アルキメデスタイリング / 双曲平面 / Schwarzの３角群 / テータ関数 |
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| Outline of Final Research Achievements |
We have studied, from the points of view of mathematics and physics, basic theory of hyperbolic Archimedean tilings on triply periodic minimal surfaces appearing as the interfaces in soft matters or mesoporous materials of nanoscopic size. In particular, we have investigated many tilings on Schwarz minimal surfaces and Schoen’s Gyroid surface. Furthermore we have given concrete expressions of the mappings between these minimal surfaces and the hyperbolic plane.
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| Free Research Field |
代数学
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