Geometry of Partial Differential Equation, Spin Structure and Twistor Theory

偏微分方程几何、自旋结构和扭量理论

• 批准号: 12304004
• 负责人: SATO Hajime
• 金额: $ 17.09万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12304004/
• 关键词: PDE; Twistor thory; Grassmannian structure; Projective contact; Lagrangean; 3^<rd> order ODE; グラスマン構造; カルタン接続; 3階の常微分方程式; 接触幾何学; 球面幾何学; 微分方程式の幾何; シュワルツ微分

As concrete examples of geometric structures related to system of geometric equations, we investigated the following pair structures by using the twistor correspondence.a) projective and Grassmannian b) projective contact and Lagrangean c) Lie contact and Lorentzian d) pure spinor and neutral structuresWe studied in detail the structures, got invariants and classified them. Further we extended the investigations to many different directions.As for a), the head investigator and Machida worked together to obtain complete invariants as elements of Spencer cohomology.Concerning b), the joint work of the head and Yoshikawa was the starting point of the investigation. Ozawa and the head found a system of partial differential equations, which gives a concrete contact transformation.As for c) and d), we got the twistor diagrams and the relation of invariants. As a new extension of the study of differential equations, we got a fundamental system for the conformal structure, which may have many applications in geometry.

作为与几何方程系统相关的几何结构的具体示例，我们通过使用扭曲器对应关系研究了以下对结构。A）射击和司法b）射击b）投影接触和lagrangean c）撒谎和洛伦兹（Lorentzian c）撒谎和Lorentzian d）纯旋转旋转和中性结构，并详细研究了详细的结构，并详细研究了无敌的人。此外，我们将调查扩展到许多不同的方向。作为a），首席调查员和Machida共同努力，作为Spencer共同体的要素。b），头部和Yoshikawa的联合工作是调查的起点。 Ozawa和Head找到了一个部分微分方程的系统，该方程给出了具体的接触转换。作为c）和d），我们得到了扭曲图图和不变性的关系。作为微分方程研究的新扩展，我们获得了共形结构的基本系统，该系统可能在几何学中具有许多应用。

项目成果

Hajime Sato: "Integrability of Contact Schwarzian Derivatives and its Linearization"Proceeding of "Geometry, Integrability and Quantization. 1. 225-228 (2000)

Hajime Sato：“接触 Schwarzian 导数的可积性及其线性化”《几何、可积性和量化》论文集。1. 225-228 (2000)

Yoshinori Machida, Hajime Sato: "Twistor thory of manifolds with Grassmannian structures"Nagoya Math.J.. 160. 17-102 (2000)

Yoshinori Machida、Hajime Sato：“具有格拉斯曼结构的流形的扭转理论”Nagoya Math.J.. 160. 17-102 (2000)

Takeshi Sasaki: "The uniformizing differential equation of the complex hyperbolic structure on the moduli space of marked cubic surfaces II"Journal of Physics A : Mathematical and General. 34. 2319-2328 (2001)

Takeshi Sasaki：“标记立方曲面模空间上复双曲结构的均匀化微分方程 II”物理学杂志 A：数学与一般。

Hiroshi Ohta: "Obstruction to and deformation of Lagrangian intersection Floer cohomology"Proceeding of KIAS workshop on "Symplectic Geometry and Mirror Symmetry". 281-309 (2001)

Hiroshi Ohta：“拉格朗日交集Floer上同调的阻碍和变形”KIAS“辛几何与镜像对称”研讨会论文集。

Hajime Sato: "Integrability of contact Schwarzian derivatives and its linearization"Proceeding of "Geometry, Integrability and Quantization" (Coral Press). 1. 225-228 (2000)

Hajime Sato：“接触 Schwarzian 导数的可积性及其线性化”《几何、可积性和量化》论文集（Coral Press）。