Study on free divisors and differential equations
Project/Area Number |
26400111
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Basic analysis
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Research Institution | Tokyo University of Agriculture and Technology |
Principal Investigator |
Sekiguchi Jiro 東京農工大学, 工学(系)研究科(研究院), 教授 (30117717)
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Co-Investigator(Renkei-kenkyūsha) |
KATO Mitsuo 琉球大学, 教育学部, 教授 (50045043)
MANO Toshiyuki 琉球大学, 理学部, 准教授 (60378594)
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Project Period (FY) |
2014-04-01 – 2017-03-31
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Project Status |
Completed (Fiscal Year 2016)
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Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
|
Keywords | 自由因子 / 平坦構造 / 複素鏡映群 / パンルベ方程式 / パンルベVI方程式 / 代数関数解 / ポテンシャル・ベクトル場 / 大久保型微分方程式 |
Outline of Final Research Achievements |
We intruduce the notion of flat sturucture which is a generalization of Frobenius manifold defined by B. Dubrovin.Potentials play a basic role in the definition of Frobenius manifold. Potential vector fields play a similar role in the definition of the flat structures. We obtain the following three results as its application. The first one is to introduce the flat coordinate on the quotient space of the affine space under the action of the well-generated irreducible complex reflection group.The second one is to establish a correspondence between solutions of generalized WDVV equtins of three variables to those of Painleve VI equation. The third one is to obtain the description of potential vector fields for algebraic solutions to Painleve VI equation.
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Report
(4 results)
Research Products
(20 results)
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[Presentation] 平坦構造と鏡映群2017
Author(s)
関口次郎
Organizer
東京電機大学数学講演会
Place of Presentation
東京電機大学(東京都足立区)
Year and Date
2017-02-20
Related Report
Invited
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[Presentation] 自由因子と微分方程式2016
Author(s)
関口次郎
Organizer
2016年度日本数学会年会
Place of Presentation
筑波大学(茨城県つくば市)
Year and Date
2016-03-16
Related Report
Invited
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[Presentation] 平坦構造入門2015
Author(s)
関口次郎
Organizer
大域解析セミナー
Place of Presentation
熊本大学理学部(熊本県熊本市)
Year and Date
2015-10-27
Related Report
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