Deepening singularity theory and low dimensional geometry
| Project/Area Number |
26400087
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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 | Kobe University |
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Principal Investigator |
Saji Kentaro 神戸大学, 理学研究科, 准教授 (70451432)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 特異点 / カスプ辺 / 接触構造 / 曲率 / 曲面論 / 表現公式 / カスプ的交差帽子 / モラン特異点 / スワローテイル / 波面 / 特異点の認識問題 / 線織面 |
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| Outline of Final Research Achievements |
For deepening singularity theory, I obtained criteria for Morin singularities for the case of the dimension of the source space and the target space is not the same. By using criteria for Morin singularities, I gave the number of right-left isotopy classes.
For low dimensional geometry, I generalized a formula for the number of singular points and the Euler characteristic to singularities of bundle homomorphisms. I also gave a normal form by only using isometric coordinate transformation of the target space for cuspidal edges and swallowtails. Moreover, I clarified the differential geometric meanings for modulus appeared in the lower degree terms. By using that form, I obtained generic configurations of asymptotic lines and characteristic lines of that singularities. I also studied singularities of solution surfaces of certain differential equation and that of surfaces which approximate the cuspidal edge.
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Report
(5 results)
Research Products
(47 results)
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[Presentation] Geometry of singular surfaces2016
Author(s)
Kentaro Saji
Organizer
School on Singularity Theory
Place of Presentation
Sao Paulo University, Sao Carlos, Brazil
Year and Date
2016-07-19
Related Report
Int'l Joint Research / Invited
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[Presentation] ４次元トポロジー2015
Author(s)
佐治健太郎
Organizer
ファイバー型モラン特異点の判定法とその応用
Place of Presentation
大阪市立大学(大阪府・大阪市)
Year and Date
2015-11-20
Related Report
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[Presentation] カスプ辺の幾何的模様2015
Author(s)
佐治健太郎
Organizer
日本数学会春季年会トポロジー分科会
Place of Presentation
明治大学 駿河台キャンパス リバティタワー
Year and Date
2015-03-21
Related Report
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