The Realization of 4-dimensional 3-Lie Algebras

In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and also give some properties about semi-simple n-Lie algebras.     

Lie代数双极化与齐性抗仿凯勒流形的新进展

本文介绍Lie代数双极化与齐性仿凯勒流形的若干新进展,并提出了若干相关问题,指出该领域可能发展的若干方向。     

微分方程及其中心流形方法的自动化简

计算机代数是应用数学的一个边缘学科 ,应用 Mathematica系统的强大的符号运算功能以及该系统提供的控制语句 ,自动实现在平衡点附近降低微分方程阶数和实行中心流形方法 ,并将该处理过程做成相关的软件包 ,简便、实用     

具有殆仿切触结构流形的新例子

本文证明了(2n+1)维连通实Lie群具有殆仿切触结构,并给出它们是可积的充要条件,从而给出这类流形一批新的例子。它们与过去已知的这类流形大都是满足某些条件的仿复流形上的主圆丛不同。     

A-扩张Lie Rinehart代数

The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary, commutative,associative algebra A.It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group,analogous to the well known relationship of Lie algebras and Lie groups.     

关于完备李群与完备李代数

孟道骥等对完备李代数作了系统的研究并已获得很多基本和重要的结果。本文给出完备李群与完备李代数的某些关系。     

李群的解析对合自同构对的分类

本文给出复单李代数的对合自同构对的分类,并利用它研究单连通,单李群的解析对合自同构对的分类.     

李群的解析对合自同构对的分类

本文给出复单李代数的对合自同构对的分类,并利用它研究单连通,单李群的解析对合自同构对的分类.     

Kaehler流形上的Hamilton力学

利用力学原理、现在微分几何理论和高等微积分把Hamihon力学推广至Kaehler流形上，建立Kaehler流形上Hamihon力学，并得到Hamilton向量场、Hamihon方程等复的数学形式．     

Real groups transitive on complex flag manifolds

Let be a complex flag manifold. The compact real form of is transitive on . If is a noncompact real form, such transitivity is rare but occasionally happens. Here we work out a complete list of Lie subgroups of transitive on and pick out the cases that are noncompact real forms of .

     

Comparison of Approximate Symmetry Methods for Differential Equations

Two current approximate symmetry methods and a modified new one are contrasted. Approximate symmetries of potential Burgers equation and non-Newtonian creeping flow equations are calculated using different methods. Approximate solutions corresponding to the approximate symmetries are derived for each method. Symmetries and solutions are compared and advantages and disadvantages of each method are discussed in detail.     

Isometric Actions of Heisenberg Groups on Compact Lorentz Manifolds

We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general construction, leading to a new example, of codimension-one actions – those for which the dimension of the Heisenberg group is one less than the dimension of the manifold. The main result is a classification of codimension-one actions, under the assumption they are real-analytic.     

Existence of homogeneous vectors on the fiber space of the tangent bundle

Let M = G/K be a homogeneous differentiable manifold. We consider the homogeneous bundle = (G, π, G/K, K) and the tangent bundle τ _G/K of M = G/K, and give some results about the existence of homogeneous vectors on the fiber space of τ _G/K, for both cases of G semisimple and weakly semisimple.      

Problems on Bieberbach Groups and Flat Manifolds

We present about twenty conjectures, problems and questions about flat manifolds. Many of them build the bridges between the flat world and representation theory of the finite groups, hyperbolic geometry and dynamical systems. In memory of Charles B. Thomas     

Geometric Integration of Ordinary Differential Equations on Manifolds

This article illustrates how classical integration methods for differential equations on manifolds can be modified in order to preserve certain geometric properties of the exact flow. Projection methods as well as integrators based on local coordinates are considered. The central ideas of this article have been presented at the 40th anniversary meeting of the journal BIT.This revised version was published online in October 2005 with corrections to the Cover Date.