More generally, the same construction allows one to construct a vector field for any Ehresmann connection on the tangent bundle.

An Ehresmann or Cartan connection supplies a lifting of curves from the manifold to the total space of a principal bundle.

In the context of Ehresmann connections, where the connection depends on a special notion of " horizontal lifting " of tangent spaces, one can define parallel transport via horizontal lifts.

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.

* An approach to connections which makes direct use of the notion of transport of " data " ( whatever that may be ) is the Ehresmann connection.

A connection on E is also determined equivalently by a linear Ehresmann connection on E. This provides one method to construct the associated principal connection.

Yet another way to define a Cartan connection is with an Ehresmann connection on the bundle E = Q ×< sub > G </ sub > G / H of the preceding section.

If x < sub > t </ sub > is a curve in M, then the Ehresmann connection on E supplies an associated parallel transport map τ < sub > t </ sub >: E < sub > x < sub > t </ sub ></ sub > → E < sub > x < sub > 0 </ sub ></ sub > from the fibre over the endpoint of the curve to the fibre over the initial point.

To show that this definition is equivalent to the others above, one must introduce a suitable notion of a moving frame for the bundle E. In general, this is possible for any G-connection on a fibre bundle with structure group G. See Ehresmann connection # Associated bundles for more details.

A principal connection can be viewed as a special case of the notion of an Ehresmann connection, and is sometimes called a principal Ehresmann connection.

A principal G-connection ω on P determines an Ehresmann connection on P in the following way.

This is an Ehresmann connection.

Conversely, an Ehresmann connection H ⊂ TP ( or v: TP → V ) on P defines a principal G-connection ω if and only if it is G-equivariant in the sense that.

Let ω be an Ehresmann connection on P ( which is a-valued one-form on P ).

** Ehresmann connection, gives a manner for differentiating sections of a general fibre bundle

The concept is due to Ehresmann and Hopf in the 1940s.

It is due to Charles Ehresmann.

The Cahiers de Topologie et Géométrie Différentielle Catégoriques ( French: Notebooks of categorical topology and categorical differential geometry ; ) is a French mathematical scientific journal established by Charles Ehresmann in 1957.

It gives rise to ( Ehresmann ) connections on any fiber bundle associated to P via the associated bundle construction.

Historically, jet bundles are attributed to Ehresmann, and were an advance on the method ( prolongation ) of Élie Cartan, of dealing geometrically with higher derivatives, by imposing differential form conditions on newly-introduced formal variables.

The founding members were all connected to the École Normale Supérieure in Paris and included Henri Cartan, Claude Chevalley, Jean Coulomb, Jean Delsarte, Jean Dieudonné, Charles Ehresmann, René de Possel, Szolem Mandelbrojt and André Weil.

Cartan connections are Ehresmann connections with additional structure which allows the parallel transport to be though of as a map " rolling " a certain model space along a curve in the manifold.

Ehresmann connections were, strictly speaking, not a generalization of Cartan connections.

Ehresmann connections were rather a solid framework for viewing the foundational work of other geometers of the time, such as Shiing-Shen Chern, who had already begun moving away from Cartan connections to study what might be called gauge connections.

The one apparent connection between the two is a score of buildings which somehow or other have survived and which naturally enough are called `` historical monuments ''.

As shown in Figure 1, there is a connection for communication between every pair of points.

In this connection, Swift, too, is drawn in for attack: `` The Author of The Conduct Of The Allies has dared to drop Insinuations about altering the Succession ''.

If art is to release us from these postulated things ( things we must think symbolically about ) and bring us back to the ineffable beauty and richness of the aesthetic component of reality in its immediacy, it must sever its connection with these common sense entities ''.

The interesting thing in this connection is that the norms upon which students tend to converge include toleration of diversity.

In connection with any claim decided by the Commission pursuant to this Title in which an award is made, the Commission may, upon the written request of the claimant or any attorney heretofore or hereafter employed by such claimant, determine and apportion the just and reasonable attorney's fees for services rendered with respect to such claim, but the total amount of the fees so determined in any case shall not exceed 10 per centum of the total amount paid pursuant to the award.

As long ago as 1851 it was pointed out by Niepce ( 1851 ) that there is a connection between the pituitary and the thyroid.

The 2% increase in retail sales in October to a 4-month high is encouraging in this connection as well as the most recent consumer survey by the National Industrial Conference Board, which shows a decided pickup in consumer spending plans.

What follows is therefore a description of three separate undertakings, the new frescoing of the gap, and the successive essays in conservation, with some discussion of problems that arose in connection with each.

It is the similarity between Estella's hands and Molly's ( `` The action of her fingers was like the action of knitting '' ) that provides Pip with a vital clue to the real identity of both and establishes a symbolic connection between the underworld of crime and the genteel cruelty of Satis House.

In this connection it is worth noting how names are sometimes obtained.

actually, there is little evidence of such personal community in Protestant congregations, as we shall see in another connection.

The secretary's greatest achievement is perhaps the rekindling of NATO realization that East-West friction, wherever it take place around the globe, is in essence the general conflict between two entirely different societies, and must be treated as such without regard to geographical distance or lack of apparent connection.

In searching for clues which might lead us to a fresh apprehension of the reality of spirit, the close connection between spirit and community is likely to prove the most fruitful.

In this connection, it has been observed that the increasing number of Irish Catholics, priests and laity, in England, while certainly seen as good for Catholicism, is nevertheless a source of embarrassment for some of the more nationalistic English Catholics, especially when these Irishmen offer to remind their Christian brethren of this good.

It is absurd of course to say that that one exclamation estranged me from the family I considered my very own, but there it hangs, a cooling void that broke our close connection with each other.

The connection with Dorians and their initiation festival apellai is reinforced by the month Apellaios in northwest Greek calendars, but it can explain only the Doric type of the name, which is connected with the Ancient Macedonian word " pella " ( Pella ), stone.

However, this story may reflect a cultural influence which had the reverse direction: Hittite cuneiform texts mention a Minor Asian god called Appaliunas or Apalunas in connection with the city of Wilusa attested in Hittite inscriptions, which is now generally regarded as being identical with the Greek Ilion by most scholars.

The connection with Latin ligare, " to bind ," is erroneous.

It has no etymological connection in French with Agincourt, Meurthe-et-Moselle ( attested as Egincourt 875 ), which is derived from another Germanic male name * Ingin -.

Like his creation the Necronomicon, Alhazred is often referenced in works that are not generally considered part of the Cthulhu Mythos, either as a subtle nod to Lovecraft or to create a connection to his world.

It is very likely that these incidents have some connection with the former Soviet Ground Forces ' phenomenon of dedovshchina ( institutionalised bullying ).

Wendell Berry is an author of several books, essays, and poems whose writing often illustrates his values which center around sustainable agriculture, healthy rural communities, and a connection to place.