2009 Fiscal Year Final Research Report
Duality of differential equations and differential geometry from the view point of singularity theory
| Project/Area Number |
19740023
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Muroran Institute of Technology |
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Principal Investigator |
TAKAHASHI Masatomo Muroran Institute of Technology, 大学院・工学研究科, 講師 (80431302)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 特異点 / 微分方程式 / 微分幾何学 / ルジャンドル特異点論 / ラグランジュ特異点論 / エンゲル・ルジャンドル変換 / 波面 / 焦面 |
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| Research Abstract |
We have studied a qualitative theory for implicit ordinary differential equations and given existence and uniqueness conditions for complete solutions of implicit ordinary differential equations. Moreover, we classified types of completely integrable second order implicit ordinary differential equations. We also have studied differential geometry and given generic classifications of tangent surfaces of Legendre curves and null curves respectively. Furthermore, we gave relationship between caustics of submanifolds and of a canal hypersurface of the submanifolds.
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