Global Analysis for Geometric Structures and Topological Invariants

几何结构和拓扑不变量的全局分析

基本信息

批准号：
09640102
负责人：
AKUTAGAWA Kazuo
金额：
$ 1.92万
依托单位：
Shizuoka 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

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640102/
关键词：
Yamabe Invariant Seiberg-Witten Equations Schottky Group Spectral Distance Moduli Space Discrete Group CR structure Abelian Differential 表現公式双曲空間調和写像重力理論ゲージ理論

项目摘要

We studied global analysis for geometric structures and topological invariants, as follows respectively.Akutagawa : He studied on the theory of Seiberg-Witten theory on compact 4-manifolds, spin^c geome-try/analysis and its application to Yamabe invariants of K_hler surfaces. He obtained some strategies for open problems on Yamabe invariants.Sato : He classified classical Schottky groups of real type of genus two into eight categories, and then obtained the fundamental domains of them and the shapes of their Schottky spaces.Kumura : He studied on the spectral distance on compact Riemannian manifolds (M, g, upsilon) with weighted measure, by using their heat kernels. He also studied on compactness of a family of and the structure of the closure of {(M_i, g_i, upsilon_i)} with respect to the spectral distance. Moreover, he applied their results to some examples.Nakanishi : He studied on the real analytic structure of the Teihm_ller spaces of 2-dimensional hyperbolic orbifolds of topologically finite. He realized the Teichm_ller spaces as real algebraic surfaces, and applied this result to the problems on the representation of mapping class groups, and the Weil-Petersson geometry.Nayatani : He studied about the canonical metrics on the domains of discontinuity of discrete groups of complex-hyperbolic isometries. He defined quaternionic analogues of CR structures and pseudo-Hermitian sturctures paticularly, and applied them the study on the cannonical metrics.Hashimoto : He studied on geometric structures induced by the Abelian differentials on Riemann surfaces. Moreover, from the viewpoint of the reduction of monodoromy of the projective structures on a Riemainn surface, he also gave a relation between the geometric structures and representation formulas of constant mean curvature surfaces.

我们研究了几何结构和拓扑不变量的全局分析，分别如下。芥川：他研究了紧致4流形的Seiberg-Witten理论、自旋^c几何/分析及其在K_hler曲面的Yamabe不变量中的应用。他获得了一些关于 Yamabe 不变量的开放问题的策略。 Sato ：他将实型 2 的经典肖特基群分为八类，然后获得了它们的基本域及其肖特基空间的形状。 Kumura ：他研究了通过使用其热核，通过加权测量紧凑黎曼流形（M，g，upsilon）上的谱距离。他还研究了 {(M_i, g_i, upsilon_i)} 族的紧致性和闭包结构相对于谱距离的关系。此外，他还将他们的结果应用到了一些例子中。 Nakanishi：他研究了拓扑有限的二维双曲轨道的 Teihm_ller 空间的实解析结构。他认识到 Teichm_ller 空间是实代数曲面，并将这一结果应用于映射类群的表示问题以及 Weil-Petersson 几何。 Nayatani ：他研究了复数离散群不连续域的规范度量-双曲等轴测图。他特别定义了CR结构和伪厄米结构的四元数类似物，并将它们应用于规范度量的研究。桥本：他研究了黎曼曲面上阿贝尔微分导出的几何结构。此外，从黎曼曲面上射影结构单射性约简的角度，他还给出了常平均曲率曲面的几何结构与表示式之间的关系。