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）在复杂的地面空间CII D1NIE D1中为孤立的奇异性。我们考虑V和真实的Hypersphere CIID2εieD2N-1I D1（X）的相交（我们为此相交）。然后m是一个非单数真实的奇数cii d2nie d2歧管。此外，在M上，ACR结构是由M。这种CR结构引起了人们的关注。实际上，该CR结构决定了正常的孤立奇异性。注意到这一点，库兰希（Kuranishi）从CR结构的争夺点（尤其是变形理论）开始了对孤立奇异性的研究。我遵循了他的界线，在1981年，如果Dimii D21R D2M = Zn-1≧7，我成功了。但是，dimii d21r d2m = zn-1≧5的情况已经打开。受Rumin在接触歧管上的工作的启发，我们（J.M.Lee和Gurfiled构建了Rumin作品的CR版本，并且通过使用Rumin Complex，我们解决了Dimii D21R D2M = Zn-1 = 5的案例。我们的复合体有效地在研究了Hodge结构的孤立奇异性结构中有效研究。

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）。