fibre bundle การใช้

• Let \ pi : T \ twoheadrightarrow B be a fibre bundle.
• In particular, it is well-defined on a general fibre bundle.
• Let E \ rightarrow M be a fibre bundle.
• Fibre bundles aren't cartesian products, but appear to be up close.
• The projection is a-principal fibre bundle.
• Let p : M \ to N be a fibre bundle with fibre F.
• The collagen fibre bundles in cattle hide are arranged in a complex weaving pattern.
• There is a corresponding notion of a graph on a fibre bundle called a section.
• His book " The Topology of Fibre Bundles " is a standard reference.
• They are twitches of a few muscle fibre bundles, which can be felt but barely seen.
• More intense retting separates the fibre bundles into elementary fibres, that can be several centimetres long.
• Fibre bundles and slit fabrics are pulled through a wet bath of resin and formed into the rough part shape.
• We first introduce the general procedure for producing an associated bundle, with specified fibre, from a given fibre bundle.
• By design, the local trivializations q _ i give a fibrewise equivalence between this quotient space and the fibre bundle p.
• The fibrils in the lamellae are directly continuous with those of the sclera, in which they are grouped together in fibre bundles.
• If the transition maps between charts of an atlas preserve a local trivialization, then the atlas defines the structure of a fibre bundle.
• An Ehresmann connection is a connection in a fibre bundle or a principal bundle by specifying the allowed directions of motion of the field.
• Kangaroo hide on the other hand has been shown to have a highly uniform orientation of fibre bundles in parallel with the skin surface.
• In general, the notion of atlas underlies the formal definition of a manifold and related structures such as vector bundles and other fibre bundles.
• One may then, as in the next section, go the other way around and derive any fibre bundle by using a fibre product.