2016 Fiscal Year Final Research Report
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
|
| 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 |
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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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| Free Research Field |
特異点論
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