Connection

Connection may refer to:

Technology

Mathematics

Connection (principal bundle)

In mathematics, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundle P over a smooth manifold M is a particular type of connection which is compatible with the action of the group G.

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. It gives rise to (Ehresmann) connections on any fiber bundle associated to P via the associated bundle construction. In particular, on any associated vector bundle the principal connection induces a covariant derivative, an operator that can differentiate sections of that bundle along tangent directions in the base manifold. Principal connections generalize to arbitrary principal bundles the concept of a linear connection on the frame bundle of a smooth manifold.

Formal definition

Let π:P→M be a smooth principal G-bundle over a smooth manifold M. Then a principal G-connection on P is a differential 1-form on P with values in the Lie algebra of G which is G-equivariant and reproduces the Lie algebra generators of the fundamental vector fields on P.

Connection (affine bundle)

Let be an affine bundle modelled over a vector bundle . A connection on is called the affine connection if it as a section of the jet bundle of is an affine bundle morphism over . In particular, this is the case of an affine connection on the tangent bundle of a smooth manifold .

With respect to affine bundle coordinates on , an affine connection on is given by the tangent-valued connection form

An affine bundle is a fiber bundle with a general affine structure group of affine transformations of its typical fiber of dimension . Therefore, an affine connection is associated to a principal connection. It always exists.

For any affine connection , the corresponding linear derivative of an affine morphism defines a unique linear connection on a vector bundle . With respect to linear bundle coordinates on , this connection reads

Since every vector bundle is an affine bundle, any linear connection on a vector bundle also is an affine connection.

If is a vector bundle, both an affine connection and an associated linear connection are connections on the same vector bundle , and their difference is a basic soldering form on . Thus, every affine connection on a vector bundle is a sum of a linear connection and a basic soldering form on .

Vicious

Vicious may also refer to:

In music:

In television:

In literature:

Other uses:

To Make a Killing

To Make a Killing is a 1988 Australian film that was also known as Vicious.

Plot

At a resort, a high school student stumbles on a series of murders.

Production

Producers Tom Broadbridge and David Hannay had decided to make a package of four exploitation films all shot on 35mm for the world video market which were all shot in late 1987. This was one of them - Broadbridge wanted Zwicky to make another script but he wanted to make his own and the producers agreed. The script was written in fit weeks and the movie was shot in four 6-day weeks in the northern suburbs of Sydney.

Release

The film was not released theatrically and went straight to video.

References

External links

Vicious (Lou Reed song)

"Vicious" is a song written by Lou Reed, released as a single in 1973 and originally featured on Transformer, Reed's second post-Velvet Underground solo album.

Origins

Lou Reed said it was Andy Warhol who inspired the song. "He said, 'Why don't you write a song called 'Vicious,'" Reed told Rolling Stone in 1989. "And I said, 'What kind of vicious?' 'Oh, you know, vicious like I hit you with a flower.' And I wrote it down literally."

Personnel

References

External links