Research on geometries of Differential Systems and Parabolic geometries

微分系统几何和抛物线几何研究

• 批准号: 23540065
• 负责人: YAMAGUCHI Keizo
• 金额: $ 3.24万
• 依托单位: Hokkaido University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540065/
• 关键词: 接触幾何学; 微分式系; 階別単純リー環; 包合系; 接触変換; 単純階別リー環; パラボリック幾何学; 単純階別りー環

We established the notion of PD-manifolds, which describes, through the concept of differentail systems, the geometry of systems of second order partial differential equations for one unknown function under contact transformations. Moerover we established two step Reduction Theorem, which is basic to Contact Geometry of Second Order.By utilizing this Reduction Theorem, we explicitly show how to construct various classes of overdetermined systems of second order partial differential equations, for which the contact equivalence problems are reduced to that of Parabolic Geometries(i.e., the geometries associated with the simple graded Lie algebras).

本文建立了PD-流形的概念，它通过微分系统的概念描述了在切触变换下关于一个未知函数的二阶偏微分方程组的几何。进而建立了二阶接触几何的基础--两步约化定理.利用这一约化定理，我们明确地给出了如何构造各类超定二阶偏微分方程组，从而将接触等价问题约化为抛物几何的问题（即，与简单分次李代数相关的几何）。

项目成果

Contact Geometry of Second Order II

二阶接触几何

• 发表时间: 2014
• 期刊: AdvancedStudies in Pure Math
• 作者: Shiga;H;西中恒和;H. Shiga;西中恒和;M. Petkova and H. Shiga;K.Yamaguchi
• 通讯作者: K.Yamaguchi

Lie temsor product manifolds

李氏乘积流形

• 发表时间: 2012
• 期刊: Demonstratio Mathematica
• 影响因子: 2
• 作者: Hajime Sato and Keizo Yamaguchi;Hironori Shiga;佐藤 拓;Hajime Sato and Keizo Yamaguchi
• 通讯作者: Hajime Sato and Keizo Yamaguchi

Lie tensor product Manifolds

李张量积流形

• 发表时间: 2012
• 期刊: Demonstratio Mathematica
• 作者: Hajime Sato and Keizo Yamaguchi

Reduction Theorems in Contact Geometry of Second Order

二阶接触几何的约简定理

• 发表时间: 2011
• 作者: 佐藤 拓;佐藤 拓;H. Shiga;Keizo Yamaguchi
• 通讯作者: Keizo Yamaguchi