1. This principal-bundle is the associated bundle of the M�bius strip. 2. See Ehresmann connection # Associated bundles for more details. 3. The companion concept to associated bundles is the "'reduction of the structure group "'of a G-bundle B. 4. Cartan connections induce covariant derivatives and other differential operators on certain associated bundles , hence a notion of parallel transport. 5. We first introduce the general procedure for producing an associated bundle , with specified fibre, from a given fibre bundle. 6. Since " ? " is a principal connection, it induces a connection on any associated bundle to " Q ". 7. The firm's lobbyist and his associates bundled contributions amounting to $ 20, 000 for McCain's presidential campaign, all perfectly legal. 8. The tangent bundle TX of a world manifold X and the associated bundle atlas of finite number of trivialization charts. 9. In other words, we ask to identify the image of the associated bundle mapping ( which is actually a functor ). 10. It gives rise to ( Ehresmann ) connections on any fiber bundle associated to " P " via the associated bundle construction.
