Singularity theory of differential geometry and its application
| Project/Area Number |
26400078
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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 | Muroran Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 特異点論 / 微分幾何学 / 曲線論 / 曲面論 / ルジャンドル特異点論 / ラグランジュ特異点論 / 曲率 / 微分方程式 / 包絡線 / 枠付き曲面 / 枠付き曲線 / 縮閉線 / ルジャンドル曲線 / 球面曲線 / 双曲空間 / ド・シッター空間 |
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| Outline of Final Research Achievements |
As singularity theory of differential geometry and its applications, we have studied a theory of Legendre curves, framed cuvres and framed surfaces. We gave the existence and the uniqueness for them by using the curvatures or the basic invariants. We investigated the evolutes, involutes, envelopes and focal surfaces for Legendre curves and framed curves. Moreover, we gave a generic classification of bifurcations of Lagrangian submanifold germs by one-parameter Lagrangian equivalence. Furthermore, we gave a generic classifications of tangent surfaces associated with Dn geometry and studied the properties from the viewpoint of differential geometry and differential equations.
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Report
(4 results)
Research Products
(31 results)
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[Presentation] 枠付き曲線と縮閉線2015
Author(s)
高橋 雅朋
Organizer
第２２回沼津研究集会
Place of Presentation
沼津高専（静岡県沼津市）
Year and Date
2015-03-10
Related Report
Invited
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[Presentation] 球面ルジャンドル曲線と縮閉線2015
Author(s)
高橋 雅朋
Organizer
接触構造、特異点、微分方程式及びその周辺
Place of Presentation
旭川市ときわ市民ホール（北海道旭川市）
Year and Date
2015-01-23
Related Report
Invited
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[Presentation] Singularities of curves2014
Author(s)
Masatomo Takahashi
Organizer
Workshop on Singularities, Geometry, Topology and Related Topics
Place of Presentation
Northeast Normal University, Changchun, China
Year and Date
2014-09-01
Related Report
Invited
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