曲率张量

Metric tensor ; curvature tensor ; asymptotic analysis ; tensor analysis

度量张量；曲率张量；渐近分析；张量分析

In Riemannian manifolds, one studies Riemannian metric, covariant derivative, Riemannian connection, basic properties of the Riemann curvature tensor, curvature forms etc.

黎曼流形部分主要涉及黎曼度量，黎曼流形的定义，切向量场的协变微分，黎曼联络，黎曼几何的基本定理，曲率张量，曲率形式等概念和理论。

The quantities ba are the covariant components of a plane tensor, called the curvature tensor of the surface

baβ是"平面张量"的协变分量，叫做该曲面的曲率张量。

They described a method to estimate the tensor of curvature of a surface at the vertices of a triangular mesh.

他们描述了一种在三角网格上任意点估计曲率张量的方法。

Principal curvatures and principal directions are obtained by computing in closed form the eigenvalues and eigenvectors of certain 3×3 symmetric matrices defined by integral formulas, and closely related to the matrix representation of the tensor of curvature.

通过计算3×3对称矩阵的特征值和特征向量可以得出主曲率和主方向，而该对称矩阵是由积分公式定义并且与曲率张量的矩阵表达密切相关。

Based on the definitions of metric tensor and curvature tensor, the full expressions of their changes are put forward with asymptotic analysis, where the metric tensor change expression coincides with Ciarlet's, and the curvature tensor change expression is described more accurately than Ciarlet's.

提出的度量张量的改变量与Ciarlet给出的一致，而曲率张量的改变量比Ciarlet给出的更精确。

To mathematically characterize the deformation of the middle surface of a shell, the metric tensor and curvature tensor ought to be investigated in detail.

为了从数学角度更好地描述壳体中性曲面如何变形，通过渐近分析和张量分析，给出了当壳体中性曲面发生形变时度量张量和曲率张量改变量的完整表达式。

In this paper, a "rigid bar relative movement model" was established to illustrate the traces of the helices in wire ropes. The angular speed of a moving particle of the model was relatives to curvature tensor to derive the curvature components and torsion of helices in multi-layer wire ropes. According to long and thin rod theory of Love and Yen-Chen's theoretical model considered the contact force and frictional force, the force-deformation or force-strain relative of wire in curved wire ropes subjected axial force is derived from the curvature components and curvature increment.

本研究改以刚杆相对运动模型，直接描述钢索中钢绞线轨迹，并且透过角速度类比曲率张量之概念，推导圆弧型多层钢索内部之钢铰线之曲率分量与扭率；之后再依据Love的细长杆理论，辅以Yen-Chen在考虑接触力及摩擦力下所修正之理论模型，以曲率及曲率增量来探讨圆弧型钢索受静态荷重作用下，钢绞线之受力与变形或应变关系。

It is shown that the atmosphere turbulence slows the downtrend of the twist parameter,gives rise the peak value of wave front curvature in the principal direction,degrades beam′s coherence and increases the spreading of beams.

根据有扭曲的各向导性高斯-谢尔模型光束在大气湍流中传播距离z处的部分相干复曲率张量给出了光束参量的表达式和详细的数值计算结果。

In this paper, we consider the n-dimensional hypersurfaces (n≥3) with vanishing Mbius form Φ.

本文考虑了S(上标 n+1)(n≥3)中具有消失Mbius形式Φ的超曲面：对具有调和曲率张量的超曲面进行分类，进而，在Mbius度量的意义下，对Einstein超曲面和具有常截面曲率的超曲面也进行了分类。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。