associated bundle sentence in Hindi
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- This principal-bundle is the associated bundle of the M�bius strip.
- See Ehresmann connection # Associated bundles for more details.
- The companion concept to associated bundles is the "'reduction of the structure group "'of a G-bundle B.
- Cartan connections induce covariant derivatives and other differential operators on certain associated bundles, hence a notion of parallel transport.
- We first introduce the general procedure for producing an associated bundle, with specified fibre, from a given fibre bundle.
- Since " ? " is a principal connection, it induces a connection on any associated bundle to " Q ".
- The firm's lobbyist and his associates bundled contributions amounting to $ 20, 000 for McCain's presidential campaign, all perfectly legal.
- The tangent bundle TX of a world manifold X and the associated bundle atlas of finite number of trivialization charts.
- In other words, we ask to identify the image of the associated bundle mapping ( which is actually a functor ).
- It gives rise to ( Ehresmann ) connections on any fiber bundle associated to " P " via the associated bundle construction.
- It proves that such jets form a fibre bundle, analogous to the tangent bundle, which is an associated bundle of a jet group.
- In a paper, written together with Ehresmann, he introduced the notion of an associated bundle and proved results known today as the exact homotopy sequence of a fibration.
- If, in addition, a right action is given on the fibre of the principal bundle, we describe how to construct any associated bundle by means of a fibre product construction.
- For this reason, in the category of fibre bundles with a structure group " G ", the principal connection contains all relevant information for " G "-connections on the associated bundles.
- The above notion can be extended to the associated bundle P \ times _ G V where " V " is a vector space transforming covariantly under some representation of " G ".
- Hence, unless there is an overriding reason to consider connections on associated bundles ( as there is, for instance, in the case of Cartan connections ) one usually works directly with the principal connection.
- The reason for the name is that a solder form solders ( or attaches ) the abstract principal bundle to the manifold " M " by identifying an associated bundle with the tangent bundle.
- One important application to note is " change of fiber " : if the " f " " ij " are all you need to make a bundle, then there are many ways to make an associated bundle.
- By applying the preceding ideas to the local 1-parameter group of diffeomorphisms defined by a vector field on " M ", and differentiating with respect to the parameter, a notion of Lie derivative on any associated bundle is obtained.
- In this way, a principal " G "-bundle equipped with a right action is often thought of as part of the data specifying a fibre bundle with structure group " G ", since to a fibre bundle one may construct the principal bundle via the associated bundle construction.
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