2019 Fiscal Year Final Research Report
Differential geometric research of regular surfaces in a wider sense
| Project/Area Number |
17K05227
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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 | Tokyo Denki University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Keywords | 曲面 / 広義正則曲面 / 特異点 / 微分幾何 |
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| Outline of Final Research Achievements |
In the academic year 2017--2019, five co-authored papers were published and one pre-print is published on the web (arXiv for math). They give a generalization distinguished from the known theory of surfaces.
The contents of the papers are researches on surfaces with singularities and mixed-type surface of spacelike-type and timelike-type. These surfaces belong to the class of `regular surfaces in a wider sense' of our theme. We studied them paying attention to mean curvature which is a differential geometric invariant.
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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 |
本研究の意義は，これまで研究されてこなかった対象に焦点を当て，いくつかの命題を示すことにより，微分幾何的曲面論における新たな側面を与えたことと言えよう．
新たな概念として「広義の正則曲面」を提唱し，広義の正則曲面およびその曲面から生じる幾何構造を研究すること，およびそれらの普遍的な理論の構築を最終目標として始められたものである．最終目標に近づくことができたことで，微分幾何的曲面論における新たな研究分野を与えることができた．
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