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 fibres 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.
Other articles related to "solder form, form":
... can be expressed by means of a vector-valued 1-form on FM called the solder form (also known as the fundamental or tautological 1-form) ... The solder form of FM is the Rn-valued 1-form θ defined by where ξ is a tangent vector to FM at the point (x,p), p-1TxM → Rn is the inverse of the frame map, and d ... The solder form is horizontal in the sense that it vanishes on vectors tangent to the fibers of π and right equivariant in the sense that where Rg is right translation by g ∈ GLn(R) ...
Famous quotes containing the word form:
“His form is fixed in my eyes,
his touch in my limbs,
his whispers in my ear,
and his heart is kept in my heart.
So what can Fate tear in two?”
—Hla Stavhana (c. 50 A.D.)