A study on curves and surfaces with singularities
Project/Area Number |
15K17547
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Geometry
|
Research Institution | Kyushu Sangyo University |
Principal Investigator |
|
Project Period (FY) |
2015-04-01 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
Keywords | 特異点 / フロンタル / 波面 / 動標構 / 縮閉線 / 開伸線 / 特異点論 / ルジャンドル曲線 / 交差帽子 / カスプ辺 / ツバメの尾 / カスプ的交差帽子 / フロント / 平面曲線 / 単純閉曲線 / 凸性 / 枠付き曲線 / ナノワード |
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.
|
Report
(4 results)
Research Products
(14 results)
-
-
-
-
-
-
[Presentation] 枠付き曲面と特異点2017
Author(s)
福永 知則
Organizer
可微分写像の特異点論とその応用
Place of Presentation
京都大学数理解析研究所
Year and Date
2017-12-07
Related Report
-
-
-
-
-
-
-
-