Web geometry, geometry of surfaces with codimension 2 and their applications to singularity theory

网络几何、余维 2 表面几何及其在奇点理论中的应用

• 批准号: 16540090
• 负责人: KUROKAWA Yasuhiro
• 金额: $ 1.79万
• 依托单位: Kure National College of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540090/
• 关键词: web; singular point; surface; asymptotic line; 4 dimension; inflection point; binary differential equation; 余次元; 余次元2

1. Geometry of surfaces with codimension 2 in 4-spaceIn this research we have investigated singularities for the asymptotic lines of generic surfaces with codimension 2 around isolated inflection points in 4-spaces. The singularities corresponds to singularities of certain class of binary differential equations. In this case the simple singularities is of type Dl, D2, D3. Also appear more degenerated singularities, which is called type D23. We give the phase portrait of type D23.2. Linearization of web structureA configurations of functions with isolated singularities gives a web structure. It seems that a finite determined theory in singularity theory is useful to study linearization problem of webs.

1。与4个跨度的编纂2的表面的几何形状这项研究研究了对通用表面的渐近线的奇异性，在4个空间中，围绕孤立的拐点围绕孤立的拐点围绕着编成imensimension 2。奇点对应于某些类别二进制微分方程的奇异性。在这种情况下，简单的奇异性是DL型，D2，D3。还出现了更多退化的奇异点，称为D23型。我们给出了D23.2型的相肖像。具有隔离奇点功能的Web结构配置的线性化提供了Web结构。似乎有限确定的奇异理论理论对于研究网的线性化问题有用。

项目成果

Singularities of differential equations of asymptotic lines on surfaces in 4-space

4-空间曲面上渐近线微分方程的奇异性

• 发表时间: 2006
• 期刊: 9th International Workshop on Real and Complex Singularities(ICMC-USP, Brazil)
• 作者: 後藤ミドリ;石川普;糸川銚;Yasuhiro Kurokawa
• 通讯作者: Yasuhiro Kurokawa