2017 Fiscal Year Final Research Report
A study on curves and surfaces with singularities
| Project/Area Number |
15K17547
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Kyushu Sangyo University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 特異点 / フロンタル / 波面 / 動標構 / 縮閉線 / 開伸線 |
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| Outline of Final Research Achievements |
I studied curves and surfaces with singularities by using moving frames. We gave the definition of evolutes and involutes of frontals in the Eucledian plane. Then we gave relations between geometric properties and singularities of frontals. Moreover, we gave a characterization of convexity of simple closed frontals in the Euclidean plane by using the curvature of the frontal. On surfaces with singularities, as a new approach to study surface with singularities, we introduced a notion of framed surfaces and constructed a fundamental theory. Especially, we defined the fundamental matrices and curvatures of framed surfaces. Then we study on a relation between a properties of the curvatures and a type of singularities.
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| Free Research Field |
特異点論
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