2014 Fiscal Year Final Research Report
Discrete differential geometry of curves from the viewpoint of discrete integrable systems
| Project/Area Number |
24540103
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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 | Fukuoka University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 差分幾何 / 曲線 / 可積分系 |
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| Outline of Final Research Achievements |
We studied deformations of discrete curves from the viewpoint of integrable systems. Especially we formulated three models of such deformations; the first is discrete deformation of planar discrete curves, the second is continuous deformation of spatial discrete curves, and the last is discrete deformation of spatial discrete curves. These deformations are governed by the discrete Burgers equation, the semi-discrete modified KdV equation, and the discrete modified KdV (or discrete sine-Gordon) equation, respectively. We illustrated our deformation theory with infinitely many examples to show the integrability of our models.
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| Free Research Field |
幾何学
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