标题： 矢量场的运动学 显示英文标题

标题： Kinematics of vector fields

摘要： 不同的（不仅符号不同）仿射联络通过非规范收缩算子为微分流形上的反变和协变张量场引入，定义了对偶基的概念，并与协变和李微分算子交换。 根据联络之间的联系，给出了线性传输的分类。 确定了矢量场的相对速度和相对加速度的概念。 通过这些运动学特征，引入了其他类型的概念，如剪切速度、剪切加速度、旋转速度、旋转加速度、膨胀速度和膨胀加速度，并在此基础上对自身平行和非各向同性（非零）矢量场进行了分类。 显示英文摘要

摘要： Different (not only by sign) affine connections are introduced for contravariant and covariant tensor fields over a differentiable manifold by means of a non-canonical contraction operator, defining the notion dual bases and commuting with the covariant and with the Lie-differential operator. Classification of the linear transports on the basis of the connections between the connections is given. Notion of relative velocity and relative acceleration for vector fields are determined. By means of these kinematic characteristics several other types of notions as shear velocity, shear acceleration, rotation velocity, rotation acceleration, expansion velocity and expansion acceleration are introduced and on their basis auto-parallel and non-isotropic (non-null) vector fields are classified.