The geometry of symmetric triad and Hermann actions

对称三元组的几何和赫尔曼作用

• 批准号: 22540108
• 负责人: IKAWA Osamu
• 金额: $ 1.41万
• 依托单位: Kyoto Institute of Technology (2012)Fukushima National College of Technology (2010-2011)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540108/
• 关键词: 対称三対; Hermann 作用; 幾何学; Hermann作用; 超極作用; 運動量写像; 荷電粒子の運動; Austere部分多様体

We introduced the notion of symmetric triad, which is a generalization of the notion of irreducible root system, and studied its fundamental properties. We defined a symmetric triad with multiplicities and showed that everysymmetric triad is obtainedfrom a commutative Hermann action. Applying these results,we studied the orbit spaces of Hermannactions on compact symmetric spaces.In particular we determined the structure of the orbit spaces of Hermann actions, and classified austere orbits. We gave a new formula which write down the moment map for holomorphic isometric action on a complete Kaehler manifold using the motion of a charged particle when the action is Hamiltonian.Further we gave a necessary and sufficient condition that a holomorphic isometric action on a complete Kaehler manifold to be Hamiltonian when the action has a fixed point. We also showed that if the first de-Rham cohomolgy group of a complete Kaehler manifold vanishes, then a holomorphic isometric action is Hamiltonian.

我们引入了对称三元组的概念，它是不可约根系概念的推广，并研究了它的基本性质。我们定义了一个具有重数的对称三元组，并证明每个对称三元组都是通过交换赫尔曼动作获得的。应用这些结果，我们研究了紧对称空间上的赫尔曼作用的轨道空间，特别是确定了赫尔曼作用的轨道空间的结构，并对简轨道进行了分类。我们给出了一个新的公式，当作用为哈密顿量时，利用带电粒子的运动，写出了完全凯勒流形上的全纯等距作用的矩图。进一步给出了完全凯勒流形上的全纯等距作用的充分必要条件当作用有固定点时流形为哈密顿量。我们还证明，如果完整凯勒流形的第一个德拉姆上同性群消失，则全纯等距作用是哈密顿量。

项目成果

A note on symmetric triad and Hermann action

关于对称三重轴和赫尔曼作用的注记

• 发表时间: 2013
• 期刊: World Scientific
• 作者: K.Shiohama;Y.Mashiko;N.Innami;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;印南信宏;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;Atsushi Fujioka and Takashi Kurose;Hitoshi Furuhata and Takashi Kurose;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;O. Ikawa;O.Ikawa and Shimabukuroe;O. Ikawa
• 通讯作者: O. Ikawa

Moment maps associated with holomorphic isometric actions on Kaehler manifolds

与凯勒流形上的全纯等距作用相关的力矩图

• DOI: 10.1007/s00022-012-0131-5
• 发表时间: 2012
• 期刊: Journal of Geometry
• 影响因子: 0.6
• 作者: K.Shiohama;Y.Mashiko;N.Innami;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;印南信宏;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;Atsushi Fujioka and Takashi Kurose;Hitoshi Furuhata and Takashi Kurose;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;O. Ikawa;O.Ikawa and Shimabukuroe;O. Ikawa;O. Ikawa
• 通讯作者: O. Ikawa

Motion of charged particles in two-step nilpotent Lie groups

两步幂零李群中带电粒子的运动

• 发表时间: 2010
• 期刊: Journal of Geometry and Symmetry in Physics
• 影响因子: 0.4
• 作者: K.Shiohama;Y.Mashiko;N.Innami;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;印南信宏;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;Atsushi Fujioka and Takashi Kurose;Hitoshi Furuhata and Takashi Kurose;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;O. Ikawa;O.Ikawa and Shimabukuroe;O. Ikawa;O. Ikawa;O. Ikawa;Osamu Ikawa;O. Ikawa
• 通讯作者: O. Ikawa

Riemann幾何学における標準形理論 -対称三対とHermann作用-

黎曼几何中的标准形式理论 - 对称三元组和赫尔曼作用 -

• 发表时间: 2010
• 作者: O.Ikawa;T.Sakai;H.Tasaki;井川治;O. Ikawa;井川治;井川治;井川治
• 通讯作者: 井川治

The geometry of symmetric triad and orbit spaces of Hermann actions

赫尔曼作用的对称三元组和轨道空间的几何

• DOI: 10.2969/jmsj/06310079
• 发表时间: 2011
• 期刊: Journal of the Mathematical Society of Japan
• 影响因子: 0.7
• 作者: K.Shiohama;Y.Mashiko;N.Innami;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;印南信宏;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;塩濱勝博;Atsushi Fujioka and Takashi Kurose;Hitoshi Furuhata and Takashi Kurose;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;黒瀬俊;O. Ikawa;O.Ikawa and Shimabukuroe;O. Ikawa;O. Ikawa;O. Ikawa
• 通讯作者: O. Ikawa