Study on free divisors and differential equations

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400111
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• 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)
• 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)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 自由因子 / 平坦構造 / 複素鏡映群 / パンルベ方程式

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.

Free Research Field

数物系科学