| Project/Area Number |
23654047
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
KATAOKA Kiyoomi 東京大学, 大学院・数理科学研究科, 教授 (60107688)
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| Project Period (FY) |
2011 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 関数方程式 / ５階偏微分方程式 / 曲面 / 円の族 / cyclide / 共形変換 / 非線形 / 解析的 / 代数曲面 / circle / differential equations / fifth order / surface / non-linear / Blum cyclide / system of equations |
|---|
| Research Abstract |
We succeeded in describing the surfaces in R^3 which include several continuous families of circles completely by some systems of nonlinear partial differential equations of order 5. We gave explicitly the very complicated form of this system of equations. Further, as applications, we obtained an upper estimate of the number of parameters classifying those surfaces, and a reduction of this system to a finite system of algebraic ordinary differential equations for 5 unknown functions of one variable.
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