A principal G-connection on a principal G-bundle P {\displaystyle P} over a smooth manifold M {\displaystyle M} is a particular type of connection that...

In mathematics, a principal bundle is a mathematical object that formalizes some of the essential features of the Cartesian product X × G {\displaystyle...

geometry and gauge theory, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect"...

in a fibre bundle or a principal bundle by specifying the allowed directions of motion of the field. A Koszul connection is a connection which defines...

case of Ehresmann connections are principal connections on principal bundles, which are required to be equivariant in the principal Lie group action....

connection for the affine group or as a principal connection on the frame bundle. The main invariants of an affine connection are its torsion and its curvature...

a system of partial differential equations for a connection on a vector bundle or principal bundle. They arise in physics as the Euler–Lagrange equations...

reinterpretations of the connection form were formulated subsequent to Cartan's initial work. In particular, on a principal bundle, a principal connection is a natural...

specialization of the general concept of a principal connection, in which the geometry of the principal bundle is tied to the geometry of the base manifold...

bundle) Connection (composite bundle) Connection (fibred manifold) Connection (principal bundle), gives the derivative of a section of a principal bundle Connection...

to a connection on the principal bundle. This notably occurs when E is the frame bundle associated to some vector bundle, which is a principal GL n {\displaystyle...

physics, gauge theory is the general study of connections on vector bundles, principal bundles, and fibre bundles. Gauge theory in mathematics should not be...

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

bundle is a fiber bundle where the fiber is the circle S 1 {\displaystyle S^{1}} . Oriented circle bundles are also known as principal U(1)-bundles,...

parameters, and so on. There are the important relations between connections on fiber bundles Y → X {\displaystyle Y\to X} , Y → Σ {\displaystyle Y\to \Sigma...

mathematics, an adjoint bundle is a vector bundle naturally associated with any smooth principal bundle. The fibers of the adjoint bundle carry a Lie algebra...

correspondence for principal bundles, that a holomorphic principal bundle over a compact Kähler manifold admits a Hermite–Einstein connection if and only if...

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...

of a differentiable principal bundle or vector bundle with a connection. Let G be a Lie group and P → M be a principal G-bundle on a smooth manifold...

Fiber bundle Principal bundle Frame bundle Hopf bundle Associated bundle Vector bundle Tangent bundle Cotangent bundle Line bundle Jet bundle Sheaf (mathematics)...

be extended to an arbitrary vector bundle, and to some principal fiber bundles. This metric is often called a bundle metric, or fibre metric. If M is a...

bundle modelled over a vector bundle Y → X. A connection Γ on Y → X is called the affine connection if it as a section Γ : Y → J1Y of the jet bundle J1Y...

bundle I-bundle Natural bundle Principal bundle Projective bundle Pullback bundle Quasifibration Universal bundle Vector bundle Wu–Yang dictionary Seifert...

connection: see Ehresmann connection, connection (principal bundle) or connection (vector bundle). It is one of the numbers that are important in the Einstein...

n-manifold M, for a given structure group G, is a principal G-subbundle of the tangent frame bundle FM (or GL(M)) of M. The notion of G-structures includes...

In mathematics, a bundle gerbe is a geometrical model of certain 1-gerbes with connection, or equivalently of a 2-class in Deligne cohomology. U ( 1 )...

holonomy), holonomy of connections in vector bundles, holonomy of Cartan connections, and holonomy of connections in principal bundles. In each of these cases...

Simpson. A Higgs bundle can be thought of as a "simplified version" of a flat holomorphic connection on a holomorphic vector bundle, where the derivative...

manifolds are fiber bundles. Therefore, a notion of connection on fibered manifolds provides a general framework of a connection on fiber bundles. Let π : Y →...

algebra bundle is a vector bundle. Examples include the tensor-algebra bundle, exterior bundle, and symmetric bundle associated to a given vector bundle, as...