Projectively flat exponential Finsler metric

INTRODUCTION One century ago, Hilbert announced his famous 23 problems. The Hilbert’s Fourth Problem is to characterize the (not-necessarily-reversible) distance functions on an open subset in ún such that straight lines are shortest paths. Distance functions induced by a Finsler metric are regarded as smooth ones. Thus Hilbert’s Fourth Problem in the smooth case is to characterize Finsler metric on an open subset in ún whose geodesics are straight lines. Finsler metric on an ope…     

Projectively flat Asanov Finsler metric

In this work, we study the Asanov Finsler metric F=α(β2/α2 gβ/α 1)1/2exp{(G/2)arctan[β/(hα) G/2]}, where α=(αijyiyj)1/2 is a Riemannian metric and β=biyj is a 1-form, g∈(-2,2), h=(1-g2/4)1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.     

On some projectively flat polynomial (α,β)-metrics

In this paper, we consider some polynomial (α,β)-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α+α1β+α2β2/α+α4β4/α3 to be projectively flat, where αi (i=1,2,4) are constants with α1≠0, α is a Riemannian metric andβ is a l-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.     

On some projectively flat polynomial （α,β）-metrics

In this paper, we consider some polynomial (α,β)-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α a1β a2β2/α a4β4/α3 to be projectively flat, where ai (i=1,2,4) are constants with a1≠0, α is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.     

黎曼几何中的某些定理在Finsler空间上的推广

本文利用空间结构方程推出了一些结果,并在此基础上无须通过繁杂的张量运算将黎曼几何中只与弧长第二变分有关的一些定理推广到Finsler空间中.     

共形平坦Finsler空间

获得了一些共形平坦Finsler空间新的判定条件。     

零曲率芬斯拉空间的共形映射

探讨两个零曲率芬斯拉空间构成共形映射的条件.     

共形平坦Finsler空间是Minkowski空间的条件

获得共形平坦Finsler空间另一判定条件及该空间是Minkowski空间的条件。     

Finsler流形中旗曲率几何性质的探讨

该文得到了Finsler流形中某点的一个领域内距离函数的表示,由此给出旗曲率的几何解释。     

Finsler空间的射影与共形映射

:获得了 Finsler空间既共形又射影另一个 Finsler空间的几个充要条件     

Hua domains and complete Einstein-K(a)hler metric

The first part of this paper we talk about the story of how to introduce the Hua domains and summarize the main results on Hua domains.The second part,the explicit complete Einstein-K(a)hler metric on the special type of Hua domains is given and the sharp estimate of holomorphic sectional curvature under this metric is also obtained.In the meantime we also prove that the complete Einstein-K(a)hler metric is equivalent to the Bergman metric on the special type of Hua domain.     

两个二维Finsler空间的测地映射

在二维Finsler空间中．借助于度量张量gij(x、y)，探讨Finsler空间的测地映射，并利用Berwald标架深入研究在各种条件下两个二维Finsler空间的测地映射问题，获得了两个Finsler空间构成测地映射的若干个新的充分必要条件。     

黎曼流形上的Toponogov定理在Finsler流形上的推广

在Finsler流形上利用活动标架法，通过沿某一方向提升，获得了弧长第二变分的表达式。将黎曼流形上的Toponogov定理推广到Finsler流形上，由此可进一步将黎曼几何中与之有关的一些定理进行推广而无须通过繁杂的张量运算。     

环面Tn上的平坦度量

研究环面Tn上的平坦度量,证明Tn上的任何平坦度量都等距于某一个标准度量     

强激光等离子体的有效度规

An effective metric is developed on the background of light field in the plasma.Consistency with effective metric and Gordon‘s metric is under the ideal fluid approximation.The validity of effective metric is verified in the limit of non-relativistic limit.Finally the effective metric for plasma electrons is obtained.     

完备度量空间中的不动点

使用w距离概念, 证明了在2个完备度量空间中2个新的不动点定理, 其中之一的结果为: 设(X, d)和(Y, ρ)是2个完备度量空间, 设p1是X上w-距离和p2是Y上w-距离. 如果T是一个从X到Y的连续映射和S是一个从Y到X的映射, 对X中所有x, x'和Y中所有y, y'以及 o＜c＜1, 满足不等式p1(STx, STx')≤cmax{p1(x, x'), p1(x, STx), p1(x', STx'),p1(x, STx')/2, p2(Tx, Tx')}和p2(TSy, TSy')≤cmax{p2(y, y'), p2(y, TSy),p2(y', TSy'), p2(y, TSy')/2, p1(Sy, Sy')}. 证明了ST在X中有惟一不动点z和TS在Y中有惟一不动点w. 这2个定理推广了 Fisher和Namdeo等人的不动点定理.     

G单位区间上的逻辑度量结构

给出了G单位区间[0,1]的定义并在其上引入了元素间的可分度的概念,讨论了其基本性质,并在此定义的基础上确定了一个度量ρ,从而（[0,1],ρ）成为一个度量空间（文中称“G单位逻辑度量空间”）,并对G单位逻辑度量空间的性质及其结构进行了详尽的讨论,并得到一些好的结果.最后,在MV单位区间上引入了类似ρ的一个度量ρ,′并证明了（[0,1],ρ′）是通常度量空间。     

关于完全有界度量集的极限状态的一个注

证明了一完全有界度量集合在Hausdorff距离之下的极限仍是完全有界集,给出了一个应用本文结果的具体例子。     

关于warped乘积S^1（a）×fS^n（b）的迷向曲率

在本文中,我们研究了warped乘积S^1（a）fS^n（b）（a^2＋b^2=1,a〉0,b〉0．n≥3）,给出了这类黎曼流形具有正迷向曲率的充分必要条件．     

关于warped乘积S^1（A）×fS^n（b）的迷向曲率

在本文中，我们研究了warped乘积S^1（A）×fS^n（b）（a^2＋b^2=1,a〉0，b〉0，n≥3），给出了这类黎曼流形具有正述向曲率的充分必要条件．