2013 Fiscal Year Final Research Report
Study on relations between differential equations and geometric structures by the method of twistor theory
| 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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| Keywords | ツイスター理論 / 微分方程式 / 幾何構造 / 旗多様体 |
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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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