将所有切向量收集起来就称为M的tangent vector field，这种情况下也称为TM的一个section(截面)；和欧氏...
理解"tangent/vectorbundle、vectorfield和section"这几个概念的关键在于把握它们之间的逻辑关系以及直观形象的理解。首先，向量丛是纤维丛的一个特殊情况，每个"纤维"都是向量空间，这定义了向量丛的基本性质。在给定流形的背景下，切丛与余切丛是特殊的向量丛，它们无需额外结构即可自然定义，但其他向量丛则...
A tangent vector field v on Rn is a function v that associates to every point p∈Rn a tangent vector to Rn based at p, i.e., a tangent vector vp∈TpRn. From: Differential Forms (Second Edition), 2014 About this pageSet alert Discover other topics ...
Hindsights: One generalization isN-symmetry fields as inPalacios and Zhang 2007andRay et al 2008. A common drawback in most linear approaches (including ours) is that the objective functional under-penalizes smoothness of the vector field in regions where the vectors have small magnitude. The wor...
每一个点的切平面上选一个过原点的矢量就够成了一个section如果这个section光滑就变成了vector field ...
网络释义 1. 切向量场 数学词汇英语翻译(S-Z) ... tangent vector 切向量tangent vector field切向量场tangent vector space 切向量空间 ... www.zftrans.com|基于20个网页
When, in particular, the ambient manifold is an open subset U of #x211D;m, a tangent vector field v on U can be identified with a map v#x2192;:U#x2192;#x211D;m, and its degree, when defined, coincides with the Brouwer degree with respect to zero of the corresponding map v#x...
1) tangent vector field 切向量场 1. Shall discuss some geometric properties of homogeneous vector fields of degree three in R 3,especially the geometric structure of thetangent vector fieldQ T( x ) on the sphere S 2 induced by such vector fields,namely the geometric distribution of singulariti...
Algebraically, a vector field on a manifold is a derivation on the ring of smooth functions. That is, a vector field acts on smooth functions and satisfies the product rule. A vector field acts on a function by the directional derivative on the function, (1) It is more precise to say...
This is known mathematically as the Cauchy-Lipschitz theorem and summarises the concept of determinism: with a given vector field, and a given starting position, there is a unique trajectory starting from that point, and this trajectory is tangent everywhere to the velocity vectors. 在数学上,这...