1) generalized isotropic Berwald curvature
广义迷向Berwald曲率
1.
In this article, some properties of generalized isotropic Berwald curvature are studied.
研究广义迷向Berwald曲率的性质, 得到: F是广义迷向Berwald曲率c(x, y)的当且仅当Dlijk =- c·kF-1hijyl,Eij =n+12c(x, y)F-1hij; 如果Lijk + c(x, y)FCijk =0, Dlijk =- c·kF-1hijyl, 则Eij =n+12c(x, y)F-1hij。
2.
In this paper, we study some properties of Finsler metric with generalized isotropic Berwald curvature and a class of special (α,β )-metric.
本文研究了一类特殊的(α,β)-度量以及具有广义迷向Berwald曲率的Finsler度量的性质。
2) isotropic Berwald curvature
迷向Berwald曲率
1.
In this paper, we discuss the relation of the isotropic Berwald curvature for pojectively related Finsler metrics F and F, the necessary and sufficient condition that F is of isotropic S-curvature is obtained from the above result.
讨论了射影相关Finsler度量F与F的迷向Berwald曲率间的关系 ,并利用这种关系得到了一个射影相关下F具有迷向S 曲率的充分必要条
3) ispotropic mean Berwald curvature
迷向平均Berwald曲率
4) Berwald curvature
Berwald曲率
1.
In this article, we mainly discuss the relation between isotropic Berwald curvatures of projectively related Finsler metrics and properties of Finsler metrics with isotropic S-curvature.
本文主要讨论了射影相关下迷向Berwald曲率间的关系和在具有迷向S-曲率的条件下Finsler度量的某些性质。
2.
Here E denotes the mean Berwald curvature of F and H is the geometric quantity which characterizes the rate of the change of E along geodesics,“|”and“.
本文首先研究了完备的Douglas空间(M,F),证明了如果其Cartan张量是有界的,且满足H=0和Ejk?lm=0,则F为Berwald度量,其中E为F的平均Berwald曲率,H为刻划E沿测地线的变化率的几何量,“|”和“。
3.
Here E is the mean Berwald curvature of F,and H is the geometric quantity which characterizes the rate of the change of E along geodesics.
l|m=0,则F为Berwald度量,其中E为F的平均Berwald曲率,H为刻划E沿测地线的变化率的几何量。
6) mean Berwald curvature
平均Berwald曲率
1.
This paper studies two important classes of(α,β)-metrics in the form F=(α+β)m+1/αm and F= α +εβ+2β2/α-β4/(3α3) on an n-dimensional manifold and proves that these two kinds of(α,β)-metrics are of isotropic mean Berwald curvature if and only if they are of isotropic S-curvature,where α=aij(x)yiyj is a Riemannian metric and β=bi(x)yi is a 1-form and m is a real number with m≠1,0,-1/n.
研究了n-维流形上两类重要的(α,β)-度量——F=(α+β)m+1/αm和F=α+εβ+2β2/α-β4/(3α3),证明了这两类(α,β)-度量具有迷向S-曲率,当且仅当它们具有平均Berwald曲率,其中α=aij(x)yiyj是黎曼度量,β=bi(x)yi是非零1-形式,m为满足m≠-1,0,-1/n的非零实数。
2.
This paper studies two kinds of important geometric quantities the mean Berwald curvature and the mean Landsberg curvature for Randers metrics, describes these important curvatures and gives a sufficient and necessary condition for Randers metric satisfying E=0 or J=0 respectively.
研究了Randers度量的两类重要的几何量———平均Berwald曲率和平均Landsberg曲率,描述了这两类重要的曲率,且分别给出了Randers度量满足E=0或J=0的充分必要条
3.
Meanwhile, we show that the mean Berwald curvature S=0 implies that the Ricci curvature Ric is quadratic in projectively flat Finsler spaces.
同时还证明了,在射影平坦Finsler空间中,平均Berwald曲率S=0意味着Ricci曲率Ric是二次齐次的。
补充资料：非迷向核
非迷向核
anisotropic kernel
非迷向核!咖即肋叩ic缺mel;a。“3oTpon。，，压pc门 定义在域k上的半单代数群(a辱braic group)G的子群D，它是极大k分裂环面SCG的中心化子的换位子群，即D=「Z。(S)，Z。(S)〕.非迷向核D是定义在k上的半单非迷向群(anisotropic梦oup);ranko=以nkG一ran城G.非迷向核的概念在研究G的人结构中起重要作用“11).设D=G，即ran从G二O，则G在k上是非迷向的;如果D=(e)，则群G称为在k上是拟分裂的(quasi一split).
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条