具有有限X-分解维数的模的同调性质

引入了左R-模M关于可解模类X以及内射余生成子W的同调维数.给出了M的X-分解维数有限的几种刻画,进而讨论了M的这两种维数之间的关系.研究了相对于有限W-分解维数的模的稳定性以及相对于模类X的模的稳定性.     

七维透镜空间为不动点集的对合

设 ( M7+ k,T)是光滑闭流形上的一个非平凡光滑对合 ,它的不动点集为 7维透镜空间 L3( p) .本文首先计算了 L 3( p)上任意向量丛的全 Stiefel-Whitney类 ,其次讨论了 ( M7+ k,T)的存在性 ,在存在的情形下 ,给出了带对合的流形 ( M7+ k,T) 协边类 .     

二维可定向流形上保持定向的周期自同胚

本文证明了二维可定向闭流形M上的任一个保持定向的周期自同胚f均可分解为若干个基本周期运动,由此推出f的较低周期轨道数目不超过2+min{4q,24q/m}(其中m为f的周期,q为M的亏格).当q>1时,f的周期必定不大于4q+2.此外,本文还证明了当q>1时,M上所有保持定向的周期自同胚的拓扑共轭类的数目有限.     

l-分解与l-维数

设R是一个有单位元的结合环,l是包含所有内射左R-模的左R-模类,则M是l-内射(约化l-内射)的当且仅当M是一个左R-模l-预覆盖(l-覆盖)E→l的核,且E是内射的.当环R关于l-预覆盖核是可经内射分解的,刻画了左l-分解、左l-维数和导出函子之间的关系,并给出应用.     

复n维射影空间的全实n维极小子流形

1.引言 设CP~n是具有Fubini-Study度规的复n维射影空间,它的常数全纯截面曲率等于4,M是CP~n的子流形。如果M上每点的切空间被CP~n的复结构J映射到该点的M的法空间中,则称M是全实子流形。又若M的平均曲率向量恒消失,则M称为全实极小子流形。Chen和Ogiue曾经证明:     

模的同态模及其同调维

S.Eilenberg 等人在五十年代后期六十年代前期对模和代数的同调维作了大量研究.设 R 与 S 是交换环 K 上的代数,则 R(?)S 也是一个 K 上的代数。当 M 与 N 分别是左R 模与左 S 模时,M(?)N 是一个左 R(?)S 模([1])。Eilenberg 等有如下结果:     

一维变换与二维变换的等价问题

一、引言定义1 设X是NM维向量(或长为NM的序列),当且仅当N×M维矩阵(X)的元素有 (1) 时,称[X]为X的矩阵表示,反之称X是(X)的向量表示。定义2 设矩阵(X)是X的矩阵表示,矩阵[R]、[P]、[Q]分别是NM×NM,N×N、M×M阶,作变换 (2)     

低维3-李代数的分类

该文研究了m≤5时特征为2的完备域上m-维3-李代数的分类,并给出了各不同构类的具体乘法表.     

含有五个反馈权值的二维细胞神经网络可实现Mosaic模式

研究一类含有五个反馈权值二维细胞神经网络系统,以系统的输出反馈权值及阈值为参数构成参数空间,引入几何方法,将此空间分解分块成有限个区域,当输出反馈权值及阈值在某一区域上时,给出系统具有M osaic解所有可能的输出函数M osaic模式的充要条件.     

超整函数族Julia集的Hausdorff维数

Stallard曾经用一族特殊的整函数说明了:超越整函数的Julia集的Hausdorff维数可以无限接近1.本文证明了该函数族的随机迭代的Julia集的Hausdorff维数也可无限接近于1.另一方面,对任意自然数M及任意实数d∈(1,2),本文给出了M个元素的整函数族其随机迭代的Julia集的Hausdorff维数等于d.     

Bcklund变换与类时极值平移曲面

首先通过选取适当的等温参数将三维Ｍｉｎｋｏｗｓｋｉ空间Ｒ２．１中的全脐点类时曲面与Ｌｉｏｕｖｉｌｅ方程相联系．其次，通过类时曲面上的类光曲线坐标将Ｒ２．１中的类时极值曲面与齐次波动方程相联系．进一步，利用Ｌｉｏｕｖｉｌｅ方程与齐次波动方程之间的Ｂａｃｋｌｕｎｄ变换，我们可以从三维Ｍｉｎｋｏｗｓｋｉ空间中一个全脐点的类时曲面得到该空间中一个类时极值平移曲面．     

Singularities of de Sitter Gauss map of timelike hypersurface in Minkowski 4-space

We study the singularities of de Sitter Gauss map of timelike hypersurface in Minkowski 4-space through their contact with hyperplanes.     

Cauchy problem on non-globally hyperbolic space-times

We consider solutions of the Cauchy problem for hyperbolic equations on non-globally hyperbolic space-times containing closed timelike curves (time machines). We prove that for the wave equation on such space-times, there exists a solution of the Cauchy problem that is discontinuous and in some sense unique for arbitrary initial conditions given on a hypersurface at a time preceding the formation of closed timelike curves. If the hypersurface of initial conditions intersects the region containing closed timelike curves, then the solution of the Cauchy problem exists only for initial conditions satisfying a certain self-consistency requirement. To Vasilii Sergeevich Vladimirov with best wishes on his 85th birthday __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 334–344, December, 2008.     

Timelike Minimal Surfaces via Loop Groups

This work consists of two parts. In Part I, we shall give a systematic study of Lorentz conformal structure from structural viewpoints. We study manifolds with split-complex structure. We apply general results on split-complex structure for the study of Lorentz surfaces.In Part II, we study the conformal realization of Lorentz surfaces in the Minkowski 3-space via conformal minimal immersions. We apply loop group theoretic Weierstrass-type representation of timelike constant mean curvature for timelike minimal surfaces. Classical integral representation formula for timelike minimal surfaces will be recovered from loop group theoretic viewpoint.     

广义de Sitter空间中的类时超曲面

利用奇点理论研究广义de Sitter空间中的类时超曲面.介绍类时超曲面的局部微分几何,定义了广义de Sitter高斯像及广义de Sitter高度函数,研究广义deSitter高度函数族的性质及广义de Sitter高斯像的几何意义,介绍了一种证明高度函数为Morse族的新方法.最后研究了类时超曲面的通有性质.     

Anti de Sitter horospherical flat timelike surfaces

We investigate a special timelike surfaces in Anti de Sitter 3-space.We call such a timelike surface an Anti de Sitter horospherical flat surface which belongs to a class of surfaces given by one parameter families of Anti de Sitter horocycle.We give a generic classification of singularities and study the geometric properties of such surfaces from the viewpoint of Legendrian singularity theory.     

三维Minkowski空间中曲面的广义Weierstrass公式

本文给出了三维Ｍｉｎｋｏｗｓｋｉ空间中一般类空曲面与类时曲面的广义Ｗｅｉｅｒ－ｓｔｒａｓｓ表示公式．     

Lorentz Geometry of 2-Step Nilpotent Lie Groups

We study the geometry of 2-step nilpotent Lie groups endowed with left-invariant Lorentz metrics. After integrating explicitly the geodesic equations, we discuss the problem of the existence of translated geodesics in those groups. A good part of the paper focuses on the existence of closed timelike geodesics in compact Lorentz 2-step nilmanifolds. Other related results, corollaries, and examples are also presented.     

On closed timelike and spacelike ruled surfaces

In this study, by using the concepts and results on spherical curves in dual Lorentzian space, we give the criterions for ruled surfaces with non‐lightlike ruling to be closed (periodic). Moreover, we obtain the necessary and sufficient conditions to guarantee that a timelike or a spacelike ruled surface is closed (periodic). Copyright © 2016 John Wiley & Sons, Ltd.     

广义de Sitter空间中的类时超曲面的切触性质

从切触几何及Legendrian奇点理论的角度研究了广义de sitter空间中的类时超曲面的切触性质及gdS-高斯像的奇点的分类和几何意义.