| Project/Area Number |
22540109
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Numazu National College of Technology |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
ISHIKAWA Goo 北海道大学, 理学研究科, 教授 (50176161)
MORIMOTO Tohru 奈良女子大学, 名誉教授 (80025460)
FUJII Kazuyuki 横浜市立大学, 総合科学部, 教授 (00128084)
TAKAHASHI Masatomo 室蘭工業大学, ひと文化系, 准教授 (80431302)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | ツイスター理論 / 微分方程式 / 幾何構造 / 旗多様体 / D_4図式 / 共形３対性 / 超幾何積分 / ガウス・マニン接続 / 次数つきリー代数表現 / 線形微分方程式系 / 外在的幾何 / D_4型旗多様体 / 共形3対性 / 重みつき微分方程式 / コーン場 / ラグランジュ・グラスマン射影双対 / リー代数表現 / 終結式 / モンジュ・アンペール系 / 非ガウス型積分 / モンジュ・アンペール方程式 |
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| Research Abstract |
An observation of twistor theory is to research relations and correspondences between different geometric structures via double fibrations. For various classes of differential equations associated with geometric structures, we study geometric meanings of equations, properties of solutions, constructions of equations and solutions. We discuss differential equations associated with cone structures, Monge-Ampere systems, equations associated with Lie algebra representations, equations associated with integrals of powers of polynomials. Treating with conformal triality from D_4 twistor diagram, we study the geometric structures, singularities, and differential equations. Treating with Kaluza-Klein space-time with (3,3) type, we study the scalar field, the vector field, the spinor field induced by the conformal SO(4,4) representation.
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