It proves that such jets form a fibre bundle, analogous to the tangent bundle, which is an associated bundle of a jet group.
22.
In general, this is possible for any " G "-connection on a fibre bundle with structure group " G ".
23.
The language of fibre bundles allows this notion of a section to be generalized to the case when " E " is not necessarily a Cartesian product.
24.
Machines pull fibre bundles through a wet bath of resin and wound over a rotating steel mandrel in specific orientations Parts are cured either room temperature or elevated temperatures.
25.
The Sudanese M�bius band in the three-sphere " S " 3 is geometrically a fibre bundle over a great circle, whose fibres are great semicircles.
26.
For an Ehresmann connection, it is possible to impose a generalized covariance principle from the beginning by introducing a Lie group acting on the fibres of the fibre bundle.
27.
If \ pi : E \ to B is a fibre bundle, then a section is a choice of point \ sigma ( x ) in each of the fibres.
28.
At this point, in order to prove that this ostensible fibre bundle is in fact a fibre bundle, it suffices to establish that it has non-singular transition functions under a change of coordinates.
29.
At this point, in order to prove that this ostensible fibre bundle is in fact a fibre bundle, it suffices to establish that it has non-singular transition functions under a change of coordinates.
30.
In that same year, Charles Ehresmann, a student of Cartan's, presented a variation on the connection as a differential form view in the context of principal bundles and, more generally, fibre bundles.
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