On the Weyl conformal invariance on manifolds with various geometric structures and its vanishing of the invariant

各种几何结构流形上的Weyl共形不变性及其不变量的消失

• 批准号: 12640082
• 负责人: KAMISHIMA Yoshinobu
• 金额: $ 2.18万
• 依托单位: Department of Mathematics, Tokyo Metropolitan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640082/
• 关键词: QCC-structure; Uniformization; Holonomy group; Developing map; Spherical CR Geometry; C-R curvature tenso; Parabolic geometry; Quaternionic hyperbolic geometry; QCC-strutme; spherical CR 幾何; 展開写像; ホロノミー群; Uniformization; C-M曲率テンサー; 4元数双曲幾何 /

1. Bochner curvature flat locally conformal Kahler manifolds: The analogue of Weyl curvature tensor on Kahler manifolds is called the Bochner curvature tensor. As it is a local invariant, the definition makes sense on locally conformal Kahler manifolds (l.c. K. manifolds). We have classified compact Bochner flat Kahler manifolds several years ago. In this continuation, we classified more generally noncompact Bochner flat l.c. K. manifolds.2. Symmetry and Global rigidity: When there exists a closed noncompact geometric flow, called Lee-Cauchy-Riemann transformations on a compact l.c. K.manifold M, we have shown a rigidity that M will be isometric to the Hopf manifold of standard type.3. Quaternionic Carnot-Caratheodory structure: We introduced a quaternionic C-C structure on (4n+3)-manifold M and constructed a curvature tensor T which is conformal invariant w. r. t. that geometric structure. If the curvature T vanishes, then we proved that M is locally modelled on the spherical pseudo-quaternionic geometry (Aut_<QC>(S^<4n+3>), S^<4n+3>). In particular, we have established the parabolic geometry on the boundary of the compactification of noncompact semisimple symmetric space of rank 1

1。Bochner曲率平坦局部保形的Kahler歧管：Kahler歧管上的Weyl曲率张量的类似物称为Bochner曲率张量。由于它是局部不变的，因此该定义在局部保形的Kahler歧管（L.C. K.歧管）上有意义。几年前，我们已将紧凑型Bochner Flat Kahler歧管分类。在此延续中，我们对Bochner Flat L.C.更一般地分类了。 K.歧管2。对称和全局刚度：当存在紧凑型L.C.上的封闭的非相对几何流量时，称为Lee-Cauchy-Riemann转换。 K.Manifold M，我们显示了M的刚度，M将与标准类型的HOPF歧管等距3。 Quaternionic carnot-caratheodory结构：我们在（4n+3）-manifold M上引入了Quaternionic C-C结构，并构建了一个曲率张量T，该曲率张紧t是共形不变w。 r。 t。几何结构。如果曲率t消失，那么我们证明了M是在球形伪Quaternionic几何形状上进行局部建模的（aut_ <QC>（S^<4n+3>），S^<4n+3>）。特别是，我们已经建立了抛物线的几何形状

项目成果

Y.Kamishima(神島芳宣): "Geomatric rigidity of Spherical hypersurfaces in quaternionic manifolds"Asian Journal of Mathematics. 3. 519-556 (1999)

Y. Kamishima (Yoshinobu Kamishima)：“四元流形中球面超曲面的几何刚性”亚洲数学杂志 3. 519-556 (1999)。

神島芽宣: "Rigidify of Ohata-Ferrand's type on Compact h on Kahler l.O.K manifolds"数理研講究録. 1223. 69-79 (2001)

Meinobu Kamishima：“Kahler l.O.K 流形上紧凑 h 的 Ohata-Ferrand 类型的刚性化”数学研究报告。1223. 69-79 (2001)。

神島芳宣: "Rigidity of Obata-Ferrand's type on Compact on Kahler L.C.K manifold"数理研講究録. 1223. 69-79 (2001)

Yoshinobu Kamishima：“Kahler L.C.K 流形上紧致型 Obata-Ferrand 类型的刚性”数学研究报告 1223. 69-79 (2001)。

Y.Kamishima(神島芳宣): "Note on locally conformal kahler surfaces"Geometriae Dedicata. 81. 11-11 (2001)

Y.Kamishima（Yoshinobu Kamishima）：“局部共形卡勒曲面的注释”Geometriae Dedicata。 81. 11-11 (2001)

Yoshinobu Kamishima: "Note on locally conformal Kahler surfaces"Geom. Dedicata. 84. 115-124 (2001)

Yoshinobu Kamishima：“关于局部共形卡勒曲面的注释”Geom。