Fiber bundles | Differential forms

Solder form

In mathematics, more precisely in differential geometry, a soldering (or sometimes solder form) of a fiber bundle to a smooth manifold is a manner of attaching the fibers to the manifold in such a way that they can be regarded as tangent. Intuitively, soldering expresses in abstract terms the idea that a manifold may have a point of contact with a certain model Klein geometry at each point. In extrinsic differential geometry, the soldering is simply expressed by the tangency of the model space to the manifold. In intrinsic geometry, other techniques are needed to express it. Soldering was introduced in this general form by Charles Ehresmann in 1950. (Wikipedia).

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Related pages

Tangent bundle | Contorsion tensor | Tautological one-form | Lie group | Principal bundle | Fiber bundle | Connection (vector bundle) | Hamiltonian mechanics | Vector-valued differential form | Associated bundle | Frame bundle | Pullback bundle | Klein geometry | Cotangent bundle | Mathematics | Bundle map | Semidirect product | Section (fiber bundle) | Contact (mathematics) | Vector bundle | Cartan connection | Torsion tensor | Differential geometry | Affine bundle | Charles Ehresmann