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Global Study of Conformal Riemannian Structures

共形黎曼结构的全局研究

基本信息

批准号：
09640084
负责人：
NAYATANI Shin
金额：
$ 1.98万
依托单位：
Tohoku University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

Shin Nayatani considered the action of a discrete transformation group of a rank one symmetric space on its boundary at infinity, and studied a canonical invariant metric defined on the domain of discontinuity. In particular, he applied it to the study of the topology of the quotient manifold when the symmetric space is complex hyperbolic space, and also formulated the quaternionic analogue of CR structure/geometry, applying it to the study of the canonical metric in the quatenionic case. He also investigated geometric structures on the Furstenberg boundaries of some higher rank symmetric spaces.Kazuo Akutagawa studied harmonic maps from hyperbolic space to a certain incomplete, negatively curved Riemannian manifold. In particular, he obtained results on the existence, uniqueness and regularity of solutions for the boundary value problem. He also made fundamental research on minimal maps between Riemannian manifolds, and obtained results on the existence and representation of minimal d … More iffeomorphisms between hyperbolic disks.Hiroyasu Izeki proved a vanishing theorem for the cohomology of flat Hilbert space bundles over a conformally flat manifold, obtained as the quotient of a spherical domain by a Kleinian group, and applied it to the study of the Hausdorff dimension of the limit set.Yasuhiro Nakagawa investigated the Bando-Calabi-Futaki character, a generalization of the Futaki character. He extended Futaki-Morita's result that interpreted the Futaki character as a Godbillon-Vey invariant, to the case of the Bando-Calabi-Futaki character.Seiki Nishikawa studied the boundary value problem for hamonic maps between homogenious Riemannian manifolds of negative curvature. In particular, he obtained results on the necessary condition which the boundary value should satisfy, the uniqueness of solution and the existence of solution for a suitable boundary value, in the case of the Carnot spaces.Shigetoshi Bando studied the existence problem for Einstein metrics on Kahler manifolds and holomorphic vector bundles as well as its relation to the stability and degeneration phenomenon. He also investigated singular geometric structures which appeared as the limit of degeneration. Less

Shin Nayatani考虑了一阶对称空间在其无穷远边界上的离散变换群的作用，并研究了定义在不连续域上的正则不变度量。特别地，他将其应用于研究对称空间为复双曲空间时商流形的拓扑，并建立了CR结构/几何的四元数模拟，将其应用于四元数情形的正则度量的研究。他还研究了一些高阶对称空间的Furstberg边界上的几何结构。Akutagawa和夫研究了从双曲空间到某种不完全的、负弯曲的黎曼流形的调和映射。特别地，他得到了关于边值问题解的存在唯一性和正则性的结果。他还对黎曼流形之间的极小映射进行了基础性研究，得到了极小d…的存在性和表示的结果。证明了共形平坦流形上的平坦Hilbert空间丛的上同调的一个消失定理，并将其应用于极限集的Hausdorff维数的研究。中川康弘研究了Bando-Calabi-Futaki特征标，它是Futaki特征标的推广。他将Futaki-Morita的结果推广到Bando-Calabi-Futaki特征标的情形，并研究了负曲率齐次黎曼流形之间的调和映射的边值问题。特别地，在卡诺空间的情况下，他得到了边值应满足的必要条件、解的唯一性和解的存在性的结果。Shigetshi Bando研究了Kahler流形和全纯向量丛上的爱因斯坦度量的存在性问题及其与稳定性和退化现象的关系。他还研究了奇异几何结构，这种结构似乎是退化的极限。较少

项目成果

期刊论文数量（57）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Kazuo Akutagawa, Kenmotsu: "Bryant type representation formula for constant mean curvature spacelike surfaces in H^3_(-c^2)" Differential Geometry and its Application. 9. 251-272 (1998)

Kazuo Akutakawa，Kenmotsu：“H^3_(-c^2) 中常平均曲率空间曲面的 Bryant 型表示公式”微分几何及其应用。

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芥川和雄: "Representlon formulas for surfaces in H^3(-C^2) and harnonis maps anising from CMC sunfaces" " Harmonic Morphisms, Harmonic Maps and Relatcd Topics "に発表予定. (1999)

Kazuo Akutakawa：“H^3(-C^2) 中曲面的表示公式和来自 CMC 太阳面的 harnonis 映射”将在“Harmonic Morphisms、Harmonic Maps and Relatcd Topics”中介绍（1999 年）。

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芥川和雄: "Spin^c geonretry the Seibag-nittcn egnations and Yamabe incariants of Kchler scnfans" Interdiseiplinarg Jrformction Sciencesに発表予定. (1999)

Kazuo Akutakawa：“Spin^c geonretry the Seibag-nittcn egnations and Yamabe incarianants of Kchler scnfans”将在 Interdiseiplinarg Jrformction Sciences 上发表（1999 年）。