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...
首先需要明确的是这几样东西的逻辑关系：这里面的基本对象是向量丛，它是一般纤维丛的一个特殊情况，即...
S2上所有点的切平面全体构成了一个bundle 模掉原点相同这个等价关系得到的商空间就是这个bundle的底也就...
Burke-M. Walker to give a formula for the -adic realization of the dg category of singularities of the zero locus of a global section of a vector bundle. In particular, we obtain a formula for the -adic realization of the dg category of singularities of the special fiber of a scheme ...
Vector Field (redirected fromTangent bundle section) Dictionary vector field [′vek·tər ‚fēld] (mathematics) The field of vectors arising from considering a system of differential equations on a differentiable manifold. A function whose range is in a vector space. ...
Related to Tangent bundle section: Whitney sum, Vector bundle, Tangent vector bundle, Zero sectionvector field n (General Physics) a region of space under the influence of some vector quantity, such as magnetic field strength, in which the quantity takes a unique vector value at every point ...
The Section tool is a simple utility that allows you to create a sectional view of your scene. Additionally, you can manipulate the section plane by dragging the translate widget and changing the cutting direction.Note The section tool is not a live-collaboration tool, it only applies to the...
Commands consist of one or two strings separated by white space, the first string being the command and the sec- ond its operand. Commands may be upper or lower case and abbreviated down to one character. Commands that affect a picture's environment (those listed before default, see below)...
Then the output consists of object files output by the assembler. Other options are passed on to one stage of processing. Some options control the preprocessor and others the compiler itself. Yet other options control the assembler and linker; most of these are not documented here, since you ...
) In fact, two results from the theory of differential forms, the Poincaré Lemma and Cartan's magic formula, make it easy to prove this; (for a vector field on any symplectic manifold (M,ω), i.e. (M,ω) does not need to be a cotangent bundle). Again writing d for the ...