Research on Contact Web Theory and Related Geometric Structures as Foundations of Theory of Differential Equations

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400067
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Nagoya University
• Principal Investigator: SATO Hajime 名古屋大学, 多元数理科学研究科, 名誉教授 (30011612)
• Co-Investigator(Renkei-kenkyūsha): OZAWA Tetsuya 名城大学, 理工学部, 教授 (20169288) ; SUZUKI Hiroshi 名古屋大学, 多元数理科学研究科, 准教授 (70235993)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: ルジャンドル織物 / グロンウォール予想 / 3階常微分方程式 / シュワルツ微分 / 接触射影幾何 / 線形化

Outline of Final Research Achievements

The uniqueness problem of linearizations of planar 3-webs under projective transformations is called Gronwall conjecture and still open for more than 100 years. Our research is concerned with Legendrian 3-webs on the 3-dimensional contact space. We proved the uniqueness of linearization map under contact projective transformations for Legendrian d-web when d is greater than 3. This solves the Gronwall conjecture in the (restricted) case above. The proof is given by showing the fundamental theorems, one by one, of contact projective geometry corresponding to those of planar projective geometry.

Free Research Field

数物系科学