2020 Fiscal Year Final Research Report
The study on the deformation space of periodic minimal surfaces and its applications
Project/Area Number |
15K04859
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Geometry
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Research Institution | Meijo University |
Principal Investigator |
Ejiri Norio 名城大学, 理工学部, 教授 (80145656)
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Project Period (FY) |
2015-04-01 – 2021-03-31
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Keywords | Riemann surface / minimal surface / flat torus / Morse index / signature |
Outline of Final Research Achievements |
In our world, soap bubbles are round. The proof is given by Mathematics. Thus, shapes except sphere do not appear. In a 3 dimensional flat torus(2 dimensional flat torus may be the face of a doughnut), what is the shape of soap bubbles? In 1992, Ross proved that Shoen's Gyroid, Schwarz' P surface and D surface are soap bubbles. We proved that H surface is a soap bubble and Schwarz'P surface is transformed into D surface under the deformation of the 3 dimensional flat torus containing P surface.
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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 |
n次元平坦トーラスの種数gの極小曲面面のMorse indexを求めるために変形空間にspecial pseudo Kaehler structure with signature (p,q)を導き、 q とMorse indexとの不等式とMorse indexを求めるalgorithmを与た。結果としてたくさんの極小曲面のMorse index が求められ応用として3次元平坦トーラスのシャボン玉の多様性がわかったことです。
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