1) scalar curvature
标量曲率
1.
In this paper,through studying Yamabe flow,we prove that for any complete noncompact locally conformally flat manifolds,if the Ricci curvature is nonnegative,the scalar curvature is bounded and the mean value of the scalar curvature satisfies some decaying condition,then the manifold is flat.
通过Yamabe流的研究,证明了对任一完备非紧局部共形平埋的黎曼流形,若Ricci曲率非负,标量曲率有界且它的平均值满足一定衰竭条件,则此流形是平坦的。
2.
Furthermore,given a compact and boundaryless n-dimensional differentiable manifold M,we show that any pointwise C-projective change from a Berwald space (M,) to a Riemann space (M,F) is trivial if the trace of the Ricci curvature Ric of with respect to F is less or equal to the scalar curvature of F.
给定一个紧致无边的n维可微流形M,证明了:对于一个从M上的Berwald度量到Riemann度量的C射影变换,如果Berwald度量的Ricci曲率关于Riemann度量的迹不超过Riemann度量的标量曲率,则该射影变换是平凡的。
4) parallel unit mean curvature vector
标准平均曲率向量
1.
In this paper we discuss the C-totally real pseudo-umbilical submanifolds with parallel unit mean curvature vector of a Sasakian space form.
文章讨论了Sasakian空间形式中标准平均曲率向量平行的C-全实伪脐子流形,得到了紧致的C-全实伪脐子流形的一个刚性结果。
5) curvature super standard
曲率超标
1.
The finite elements stress analysis and calculations were done for 1 500 m3 curvature super standard sphere tank under design and hydrostatic testing pressure,and strength check had been executed according to the stress analysis and design method.
对1500m3曲率超标球罐在水压试验和设计压力工况下进行了有限元应力分析计算,并根据应力分析设计方法进行了强度校核。
6) curvature index
曲率指标
1.
The results show that(1) the curvature index CI7 and shape factor F8 can be used to determine the subsoil modulus;(2) crack and interface sliding have no influence on CI7-F8 characteristic curve;(3) the depth of rigid layer has impact on CI7-F8 characteristic curve when the depth is lower than 7 m.
计算结果表明:土基模量可由曲率指标CI7和形状指标F8确定;开裂和层间滑移对CI7-F8关系曲线没有影响;当刚性层深度小于7 m时,刚性层深度将对CI7-F8关系曲线产生影响。
补充资料：标量曲率
标量曲率
scalar curvature
体里州革走义.坛.碑.加re;c“”几.此翻。~二，。一，一称攀量吵半，既~流形在一点，的 Ricci张量(Ricci tensor)关于度量张量g的迹.标量曲率s(p)与Rieci曲率(Ricei eurvat眠);和截面曲率(sectional curvature)k通过公式 “(p，一，互尹(“，，一买.“(“f，“，)联系起来，这里e:，…，e。是切空间的一个规范正交基.用等价的Einstein记号，这些方程的形式为 s(夕)=夕‘，R。，二夕厅g“R*。，，这里R。和R、，，，分别是Ricci张量和曲率张量的分量，g。是度量张量的反变分量.[补注] 〔AI 1 Kobaydshi，5 .and No加zu，K.，Fo山记ations of d江ferent功1 geometry，l一2，WIlev(interse哪ee)， 1963一1969.【译注】 这里曲率张量的分量R*。，与文献[AI]中的定义相差一符号.目前大都采用IAI]的定义，因此标量曲率的公式为 S(夕)一。“R，，二。“。“R*。，，· 潘养廉译沈一兵校
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