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-bundleP over a smooth manifoldM is a particular type of connection which is compatible with the action of the group G.
Let π:P→M be a smooth principal G-bundle over a smooth manifoldM. Then a principal G-connection on P is a differential 1-form on Pwith values in the Lie algebra of G which is G-equivariant and reproduces the Lie algebra generators of the fundamental vector fields on P.
An affine bundle is a fiber bundle with a general affinestructure 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 .
"Connection" is a song released by the Britpop group Elastica. It was originally released in 1994 as a single and the album version was not released until 1995 on their self-titled debut.
The song was the subject of controversy, due to its overt similarity to another band's work. The intro synthesizer part (later repeated as a guitar figure) is lifted from the guitar riff in Wire's "Three Girl Rhumba" and transposed down a semitone. A judgment resulted in an out-of-court settlement and the credits were rewritten.
The root of the word "divine" is literally "godly" (from the Latin deus, cf. Dyaus, closely related to Greek zeus, div in Persian and deva in Sanskrit), but the use varies significantly depending on which deity is being discussed. This article outlines the major distinctions in the conventional use of the terms.
Harris Glenn Milstead, better known by his stage name Divine (October 19, 1945 – March 7, 1988), was an Americanactor, singer and drag queen. Closely associated with the independent filmmaker John Waters, Divine was a character actor, usually performing female roles in cinematic and theatrical appearances, and adopted a female drag persona for his music career.
Born in Baltimore, Maryland to a conservative middle-class family, Milstead developed an early interest in drag while working as a women's hairdresser. By the mid-1960s he had embraced the city's countercultural scene and befriended Waters, who gave him the name "Divine" and the tagline of "the most beautiful woman in the world, almost." Along with his friend David Lochary, Divine joined Waters' acting troupe, the Dreamlanders, and adopted female roles for their experimental short films Roman Candles (1966), Eat Your Makeup (1968), and The Diane Linkletter Story (1969). Again in drag, he took a lead role in both of Waters' early full-length movies, Mondo Trasho (1969) and Multiple Maniacs (1970), the latter of which began to attract press attention for the group. Divine next starred in Waters' Pink Flamingos (1972), which proved a hit on the U.S. midnight movie circuit, became a cult classic, and established Divine's fame within the American counterculture.
Divine was an American R&B girl group formed in 1996 who are best known for their 1998 hitsingle "Lately". Group members include Kia Thornton, Nikki Bratcher and Tonia Tash. All three women were teenagers when they were recruited by Pendulum Records owner Ruben Rodriguez to form Divine who were ultimately released on his label Red Ant Entertainment.
of G which is G-equivariant and reproduces the Lie algebra generators of the fundamental vector fields on P.
be an 
. A 
on 
is called the affine connection if it as a section 
of the 
of 
is an affine bundle morphism over 
. In particular, this is the case of an 
of a 
on 
of affine transformations of its typical fiber 
of dimension 
. Therefore, an affine connection is associated to a 
of an affine morphism 
on 
, this connection reads
are
connections on the same vector bundle 
. Thus, every affine
connection on a vector bundle 
