geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically...

{\displaystyle M} . Then a principal G {\displaystyle G} -connection on P {\displaystyle P} is a differential 1-form on P {\displaystyle P} with values in the Lie...

Look up connections in Wiktionary, the free dictionary. Connections may refer to: Connection (disambiguation), plural form “Connections: The Marcello...

Ehresmann connection Grothendieck connection Levi-Civita connection Connection form Connection (fibred manifold) Connection (principal bundle) Connection (vector...

In mathematics, a metric connection is a connection in a vector bundle E equipped with a bundle metric; that is, a metric for which the inner product of...

In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector...

for an Ehresmann connection is that it can be represented as a differential form, in much the same way as the case of a connection form. If the group acts...

In differential geometry, the curvature form describes curvature of a connection on a principal bundle. The Riemann curvature tensor in Riemannian geometry...

manifold M. This principal bundle is equipped with a connection form ω, a gl(n)-valued one-form which maps vertical vectors to the generators of the right...

mathematics, and especially differential geometry and gauge theory, a connection on a fiber bundle is a device that defines a notion of parallel transport...

defined connection. The exterior product of a k-form α and an ℓ-form β, denoted α ∧ β, is a (k + ℓ)-form. At each point p of the manifold M, the forms α and...

a bilinear form B : X × X → F, with the relation B(x, y) = u(x)(y). By defining the transpose of this bilinear form as the bilinear form tB defined by...

A form-fit, form-locking or form-closed connection is a type of mechanical connection between two parts (such as the head of a screw with a screwdriver)...

In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of...

connection as a Cartan connection. For Lie groups, Maurer–Cartan frames are used to view the Maurer–Cartan form of the group as a Cartan connection....

in two common forms: the Levi-Civita spin connection, when it is derived from the Levi-Civita connection, and the affine spin connection, when it is obtained...

Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold that preserves the...

quantity. The curvature form F, a Lie algebra-valued 2-form that is an intrinsic quantity, is constructed from a connection form by F = d A + A ∧ A {\displaystyle...

forms can be viewed as R-valued differential forms. An important case of vector-valued differential forms are Lie algebra-valued forms. (A connection...

theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets). Galois connections find applications...

In mathematics, a volume form or top-dimensional form is a differential form of degree equal to the differentiable manifold dimension. Thus on a manifold...

Lie-algebra-valued form is a differential form with values in a Lie algebra. Such forms have important applications in the theory of connections on a principal...

parallel transport, covariant derivative and connection form. These concepts were put in their current form with principal bundles only in the 1950s. The...

single point then the Maurer–Cartan form can also be characterized abstractly as the unique principal connection on the principal bundle G. Indeed, it...

connection on ⁠ κ {\displaystyle \kappa } ⁠. The curvature of this connection is the 2-form defined by ρ ( X , Y ) = def Ric ⁡ ( J X , Y ) {\displaystyle \rho...

vector fields and 1-forms simultaneously. A frequent example application of this general rule is showing that the Levi-Civita connection, which is a mapping...

array of numbers describing a metric connection. The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed...

structure. This is called the Chern connection on E {\displaystyle E} . The curvature of the Chern connection is a (1, 1)-form. For details, see Hermitian metrics...

which has as "dynamical" fields a 2-form B taking values in the adjoint representation of G, and a connection form A for G. The action is given by S =...

algebra is affine space. This is also the intimate connection between exterior algebra and differential forms, as to integrate we need a 'differential' object...