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1) mean Berwald curvature 点击朗读

平均Berwald曲率

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。

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

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。

2) ispotropic mean Berwald curvature 点击朗读

迷向平均Berwald曲率

3) Berwald curvature 点击朗读

Berwald曲率

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。

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“。

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。

4) isotropic Berwald curvature 点击朗读

迷向Berwald曲率

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

5) generalized isotropic Berwald curvature 点击朗读

广义迷向Berwald曲率

In this article, some properties of generalized isotropic Berwald curvature are studied. 点击朗读

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。

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。

6) mean curvature 点击朗读

平均曲率

Study on hypersurface with constant mean curvature in sphere; 点击朗读

球面上的常平均曲率超曲面

The properties of a riemannian foliation with parallel mean curvature on a Riemannian manifold;

常曲率空间中具有相同常平均曲率的黎曼叶状结构的一些性质

The classification of space-like surfaces with parallel mean curvature vector of an indefinite space form;

不定空间形式中具平行平均曲率向量的类空曲面(英文)

更多例句>>

补充资料：平均曲率

平均曲率
mean cunafure

　　平均ee率[~e一臼此;epe刀田皿.印棚3.a]，3维Euclid空间R’中曲面小2的该曲面点A处主曲率(prmc币alcun瓜ture)k，与k:和之半: k，+k， H(A、二一_ 2对于EucUd空间R”+’中的超曲面。”，此公式可推广为: k，+…+k_ H‘A、二一 n其中k‘(j=l，…，n)是所给超曲面在点A任中”处的主曲率. R3中曲面的平均曲率可通过该曲面的第一和第二基本形式的系数表示: 1 LG一ZMF+NE H(A)二之二二二‘一二二七二一二二二全匕 2 EG一F乙其中E，F，G是在点A。中2处计算的第一基本形式(肠tfi功dsl拙ntal fbxm)的系数，L，M，N是该点处第二基本形式(second加次ha众浏园form)的系数.在所给曲面由方程Z=f(x，y)定义的特殊情形，平均曲率可用下述公式计算: H(A)= 卜十图’)典一2李李-业二、「1+国’}斗 L\oy/J ox一ox oy口x口yL\口x/J口y‘ 「1、r李、’十了鱿、’1’‘， L‘\刁x/’\a夕/」此公式推广到R”干’中由方程x。+、=f(x，，…，x。)定义的超曲面中”如下: H(A)，女rl+。2-位Z力2〕里本一争皿』五一望立- ‘习L一\口工‘/」dx了‘.界，口x‘dxz dx，dxz (l+p’)’12其中，2一}gtadf}2一r李、’+…、{共)’. ·扩一\似，/\叔。/ 几.A.C”江opoB撰【补注l对于n维E珑lid空间中余维数为”一功>1的m维子流形M，平均曲率推广为平均曲率法向量(n笼习n cun旧t切吧nont自1)概念: 、，一生”犷「TrA(。‘、1。. m]=!其中e:，·，e。一。是M在p处的法空间(见法空间(曲面的)(nom以lsP毗(to as切成‘e))的标准正交标架，A( ej):T，(M)~T，(M)(T，(M)为M在p处的切空间)是M在p处沿e，方向的形状算子(s恤pe oPemtor)，它与M在p处的第二基本张量V由“相联系.
　　

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

平均曲率<测> 常平均曲率曲面曲面的平均曲率平行平均曲率

常平均曲率平均曲率流全平均曲率平均曲率H 总平均曲率平均曲率型

说明：双击或选中下面任意单词，将显示该词的音标、读音、翻译等；选中中文或多个词，将显示翻译。
	您的位置：首页 -> 词典 -> 平均Berwald曲率 1) 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。 2) ispotropic mean Berwald curvature 迷向平均Berwald曲率 3) 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。 4) 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 5) 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。 6) mean curvature 平均曲率 1. Study on hypersurface with constant mean curvature in sphere; 球面上的常平均曲率超曲面 2. The properties of a riemannian foliation with parallel mean curvature on a Riemannian manifold; 常曲率空间中具有相同常平均曲率的黎曼叶状结构的一些性质 3. The classification of space-like surfaces with parallel mean curvature vector of an indefinite space form; 不定空间形式中具平行平均曲率向量的类空曲面(英文) 更多例句>> 补充资料：平均曲率平均曲率 mean cunafure 　　平均ee率[~e一臼此;epe刀田皿.印棚3.a]，3维Euclid空间R’中曲面小2的该曲面点A处主曲率(prmc币alcun瓜ture)k，与k:和之半: k，+k， H(A、二一_ 2对于EucUd空间R”+’中的超曲面。”，此公式可推广为: k，+…+k_ H‘A、二一 n其中k‘(j=l，…，n)是所给超曲面在点A任中”处的主曲率. R3中曲面的平均曲率可通过该曲面的第一和第二基本形式的系数表示: 1 LG一ZMF+NE H(A)二之二二二‘一二二七二一二二二全匕 2 EG一F乙其中E，F，G是在点A。中2处计算的第一基本形式(肠tfi功dsl拙ntal fbxm)的系数，L，M，N是该点处第二基本形式(second加次ha众浏园form)的系数.在所给曲面由方程Z=f(x，y)定义的特殊情形，平均曲率可用下述公式计算: H(A)= 卜十图’)典一2李李-业二、「1+国’}斗 L\oy/J ox一ox oy口x口yL\口x/J口y‘ 「1、r李、’十了鱿、’1’‘， L‘\刁x/’\a夕/」此公式推广到R”干’中由方程x。+、=f(x，，…，x。)定义的超曲面中”如下: H(A)，女rl+。2-位Z力2〕里本一争皿』五一望立- ‘习L一\口工‘/」dx了‘.界，口x‘dxz dx，dxz (l+p’)’12其中，2一}gtadf}2一r李、’+…、{共)’. ·扩一\似，/\叔。/ 几.A.C”江opoB撰【补注l对于n维E珑lid空间中余维数为”一功>1的m维子流形M，平均曲率推广为平均曲率法向量(n笼习n cun旧t切吧nont自1)概念: 、，一生”犷「TrA(。‘、1。. m]=!其中e:，·，e。一。是M在p处的法空间(见法空间(曲面的)(nom以lsP毗(to as切成‘e))的标准正交标架，A( ej):T，(M)~T，(M)(T，(M)为M在p处的切空间)是M在p处沿e，方向的形状算子(s恤pe oPemtor)，它与M在p处的第二基本张量V由“相联系. 　　说明：补充资料仅用于学习参考，请勿用于其它任何用途。参考词条平均曲率<测> 常平均曲率曲面曲面的平均曲率平行平均曲率

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