Research on global structures of Lorentzian semi-symmetric spaces

洛伦兹半对称空间的整体结构研究

• 批准号: 16540089
• 负责人: GOTO Midori
• 金额: $ 2.05万
• 依托单位: Fukuoka 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: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540089/
• 关键词: Lorentzian metric; Lorentz manifold; semi-symmetric space; Liouville metric; Liouville manifold; Liouville surface; generalized Liouville manifold; Lorentz-Liouville構造; Liouville構造; generalized-Liouville構造; ローレンツ型擬対称空間; 局所共形平坦; ローレンツ曲面; 共形平坦

In the study of Riemannian geometry, it is important to investigate geodesic behaviors, which effect on topological structures of manifolds. Curvatures (local notion) of Riemannian manifolds often have influence on topological structures (global notion). What about in Lorentz geometry? From the viewpoints, we investigate Lorentz geometry. Global behaviors of geodesics are not well-known for most manifolds. Hence, investigations of Liouville structure, which have been initiated by C.G.F.Jacobi in 1866, turn out to be important.Our main results which we obtained during the period are in the following two forthcoming papers, both of which are joint works by Midori Goto and Kunio Sugahara :1. Generalized Liouville manifolds.In this paper, we defined a new notion, the generalized Liouville structure, and succeeded to prove that all quadric surfaces in the n+1 dimensional Cartesian space possess the generalized Liouville structures with respect to the indefinite/definite metrics, besides the Eucledian metric. In the classification of Riemann-Liouville surfaces the number of singularities plays a key role in Kiyohara's and Igarashi-Kiyohara-Sugahara's papers about Liouville surfaces. We proved that there is no such kind of singularity in the Lorentz-Liouville surface. For generalized Liouville maniflods of dimension >2, we determined the set of singularities. The classification problems for generalized Liouville manifolds are supposed to be made clear.2. A remark on Lorentzian metrics of 3-dimensional manifolds.In the paper, we see that there are 3-dimensional Riemannian manifolds whose Riemannian connections coincide with the Lorentzian connections associated with the naturally defined Lorentzian metrics. Reviewing the result, we conjecture that, except for the case of constant curvature, there may not be expected any relations between curvatures and topological structures.

在黎曼几何形状的研究中，重要的是研究地质行为，这对歧管的拓扑结构产生了影响。黎曼流形的曲率（局部概念）通常会对拓扑结构（全球概念）产生影响。在Lorentz几何形状中呢？从角度来看，我们研究洛伦兹的几何形状。大多数歧管的全球地球学行为并不是众所周知的。因此，C.G.F. Jacobi于1866年对Liouville结构进行的调查非常重要。我们在此期间获得的主要结果是在以下两篇即将发表的论文中，这两者都是Midori Goto和Kunio Sugahara的联合作品：1。在本文中，我们定义了一个新的概念，即广义的liouville结构，并成功证明了n+1维笛卡尔空间中的所有四个二次表面都具有相对于不确定/确定的衡量指标的广义liouville结构。在Riemann-Liouville的分类中，奇异性的数量在Kiyohara和Igarashi-Kiyohara-Sugahara关于Liouville表面的论文中起着关键作用。我们证明了Lorentz-Liouville表面没有这种奇异性。对于> 2的广义liouville散像，我们确定了一组奇异性。普遍的liouville歧管的分类问题应该明确。2。关于洛伦兹（Lorentzian）三维流形的指标的评论。在论文中，我们看到有三维riemannian流形的歧管，其riemannian连接与洛伦兹（Lorentzian）的连接相吻合，与洛伦兹（Lorentzian）的连接相吻合。回顾结果，我们猜想，除了持续曲率的情况外，曲率和拓扑结构之间可能没有任何关系。

项目成果

Magnetohydrodynamics approaches to measure-valued solutions of the two-dimensional stationary Euler equations

二维稳态欧拉方程测量值解的磁流体动力学方法

• 期刊: Bull. Inst. Math. Sinica (New Series) (印刷中)
• 作者: Akira SASAMOTO;Takayuki SUZUKI;Yoshihiro NISHIMURA;海津聰;藤間 昌一;笹本 明;Satoshi Kaizu;笹本明;川添良幸;Takahito Nishiyama;Takahiro Nishiyama;Takahiro Nishiyama;後藤 ミドリ;Takahiro Nishiyama;西原 賢;西山 高弘;西山 高弘;西原 賢;西原 賢 他4名;Takahiro Nishiyama
• 通讯作者: Takahiro Nishiyama

Global structures of compact conformally flat semi-symmetric spaces of dimension three and of non-constant curvature

三维非等曲率紧致共形平坦半对称空间的整体结构

• 期刊: Birkhauser社、Progress in Math.シリーズ 印刷中
• 作者: Akira SASAMOTO;Takayuki SUZUKI;Yoshihiro NISHIMURA;海津聰;藤間 昌一;笹本 明;Satoshi Kaizu;笹本明;川添良幸;Takahito Nishiyama;Takahiro Nishiyama;Takahiro Nishiyama;後藤 ミドリ;Takahiro Nishiyama;西原 賢;西山 高弘;西山 高弘;西原 賢;西原 賢 他4名;Takahiro Nishiyama;Takahiro Nishiyama;西山 高弘;後藤 ミドリ
• 通讯作者: 後藤 ミドリ

An integral transform whose kernel is a stream function of a steady Euler flow with axisymmetry

一种积分变换，其核是轴对称稳定欧拉流的流函数

• 发表时间: 2007
• 期刊: Z. Angew. Math. Phys. 58
• 作者: Akira SASAMOTO;Takayuki SUZUKI;Yoshihiro NISHIMURA;海津聰;藤間 昌一;笹本 明;Satoshi Kaizu;笹本明;川添良幸;Takahito Nishiyama
• 通讯作者: Takahito Nishiyama

A relaxation method for constructing a Beltrami flow in a bounded domain

有界域内构造贝尔特拉米流的松弛方法

• 发表时间: 2005
• 期刊: J.Math.Phys. 46・8
• 作者: Akira SASAMOTO;Takayuki SUZUKI;Yoshihiro NISHIMURA;海津聰;藤間 昌一;笹本 明;Satoshi Kaizu;笹本明;川添良幸;Takahito Nishiyama;Takahiro Nishiyama;Takahiro Nishiyama;後藤 ミドリ;Takahiro Nishiyama;西原 賢;西山 高弘
• 通讯作者: 西山 高弘

A Hahn-Banach extension theorem for entire functions of nuclear type

核型全部函数的Hahn-Banach扩展定理

• 发表时间: 2004
• 期刊: J.Korean Math.Soc. 41
• 作者: Akira SASAMOTO;Takayuki SUZUKI;Yoshihiro NISHIMURA;海津聰;藤間 昌一;笹本 明;Satoshi Kaizu;笹本明;川添良幸;Takahito Nishiyama;Takahiro Nishiyama;Takahiro Nishiyama;後藤 ミドリ;Takahiro Nishiyama;西原 賢;西山 高弘;西山 高弘;西原 賢
• 通讯作者: 西原 賢