3-流形上的Poisson矩阵及其应用  

Poisson Matrices on 3-Manifolds and Their Applications to 3-CPM Manifolds

作　　者：李洪军[1] 

机构地区：[1]西安交通大学理学院,西安710049

出　　处：《数学学报（中文版）》2004年第2期403-412,共10页Acta Mathematica Sinica：Chinese Series

摘　　要：本文利用可定向3-流形切丛的平凡性,在3维几何上建立了一种整体标架法.对于3-流形上任一整体切标架,定义了一个Poisson矩阵,并给出:Poisson矩阵在标架改变时的变化规律.以Poisson矩阵为原始数据,计算了相应Riemannian度量各种曲率的具体表达式.对于具有常值Poisson矩阵的一类3-流形,这个方法被用来讨论它们的拓扑结构.它们基本上都是3维李群在其离散子群左平移作用下的商空间.In this paper, the existence of a global tangent frame on every oriented and connected smooth 3-manifold will be used to develop a global frame method in 3-dimensional geometry and topology. Corresponding to each global tangent frame, we define a Poisson matrix on the 3-manifold. And using it as an initial data, we give an explicit expression of all the curvatures for some Riemannian metric. The method is applied to 3-manifolds with constant Poisson matrix. Such 3-manifolds are essentially the homogeneous spaces of 3-dimensional Lie groups.

关 键 词：整体标架 Poisson矩阵 曲率 齐性空间 

分 类 号：O186[理学—数学]