The application of the Rumin complex to isolated sirgularities

瘤胃复合体在孤立性规则中的应用

• 批准号: 10640211
• 负责人: AKAHORI Takao
• 金额: $ 0.32万
• 依托单位: Himeji Institute 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: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640211/
• 关键词: CR structure; pseudo-convex; isolated singularity; 接触幾何; 変形理論

Let (v, x) be an isolated singularity in a complex enclidean space CィイD1NィエD1. We consider the intersection of v and the real hypersphere SィイD2εィエD2ィイD12N-1ィエD1(x) (we write M for this intersection). Then M is a non singular real odd dimensional CィイD2NィエD2 manifold. Furthermore, on M, aCR structure is induced from M. This CR structure is of interest. In fact, this CR structure determines the normal isolated singularity. Noting this point, Kuranishi initiated his research on isolated singularities from the point of vie of Cr structures (especially, deformation theory). I followed his line, and in 1981, I succeeded if dimィイD21R ィエD2M=zn-1≧7. But the case dimィイD21R ィエD2M=zn-1≧5 has been left open. Inspired by Rumin's work on contact manifolds, we (with J.M.Lee and Gurfiled constructed a CR version of Rumin's work , and by using the Rumin complex, we settle the case dimィイD21R ィエD2M=zn-1=5. Our complex is efficient in studying the complex structures of isolated singularities from the point of view of Hodge structure. But this is still in preparation.

令 (v, x) 为复闭环空间 D1N-1D1 中的孤立奇点，我们考虑 v 与实超球面 D2N-1D1(x ) 的交集（我们将这个交集写为 M ），则 M 是非奇异点。此外，在 M 上，由 M 导出 aCR 结构。该 CR 结构为事实上，这种 CR 结构决定了正常的孤立奇点，Kuranishi 从 Cr 结构的角度开始了他对孤立奇点的研究（特别是变形理论），并于 1981 年，如果dimD21R D2M=zn-1≧7我就成功了，但是D21R D2M=zn-1≧5的情况已经留下了。受 Rumin 在接触流形方面的工作的启发，我们（与 J.M.Lee 和 Gurfiled 一起构建了 Rumin 工作的 CR 版本，并通过使用 Rumin 复合体，我们解决了 dimiD21R ieD2M=zn-1=5 的情况。我们的复合体在以下方面是有效的。从霍奇结构的角度研究孤立奇点的复杂结构但这仍在准备中。

项目成果

赤堀隆夫: "Real analyticity of the canonical versal deformation of CR-strnetures" Pacific J.of Math.Vol.185-1. 33-45 (1998)

Takao Akahori：“CR 结构的规范通用变形的真实分析”Pacific J.of Math.Vol.185-1（1998）。

Takao Akahori: "Real analyticity of the canonical deformations of CR-structures"Pacific Journal of Mathematics. Vol.185, No.1. 33-45 (1998)

Takao Akahori：“CR 结构规范变形的真实分析”太平洋数学杂志。

赤堀隆夫: "Real analyticity of the canonical versal deformations of CR-structures"Pacific Journal of Mathematics. 185. 33-45 (1998)

Takao Akahori：“CR 结构的规范通用变形的真实分析性”太平洋数学杂志 185. 33-45 (1998)。

赤堀隆夫: "A smoothness of deformations of normal strongly pseudo-convex CR structures"Kyushu J. of Mathematics. 52. 413-438 (1998)

Takao Akahori：“正常强伪凸 CR 结构变形的平滑性”九州数学杂志 52. 413-438 (1998)。

赤堀隆夫: "A Smoothness of deformations of normal strongly Psendo-cornex CR structures"Kyushu Journal of Mathematics. 52・2. 413-418 (1998)

Takao Akahori：“通常强Psendo-cornex CR结构的变形的平滑性”九州数学杂志52・2（1998）。