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In older literature, the term linear connection is occasionally used for an Ehresmann connection or Cartan connection on an arbitrary fiber bundle, [1] to emphasise that these connections are "linear in the horizontal direction" (i.e., the horizontal bundle is a vector subbundle of the tangent bundle of the fiber bundle), even if they are not ...
The following is a list of linear integrated circuits. Many were among the first analog integrated circuits commercially produced; some were groundbreaking innovations, and many are still being used.
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A G-connection on E is an Ehresmann connection such that the parallel transport map τ : F x → F x′ is given by a G-transformation of the fibers (over sufficiently nearby points x and x′ in M joined by a curve). [5] Given a principal connection on P, one obtains a G-connection on the associated fiber bundle E = P × G F via pullback.
Therefore, an affine connection is associated to a principal connection. It always exists. For any affine connection Γ : Y → J 1 Y, the corresponding linear derivative Γ : Y → J 1 Y of an affine morphism Γ defines a unique linear connection on a vector bundle Y → X. With respect to linear bundle coordinates (x λ, y i) on Y, this ...
This is a list of well-known data structures. For a wider list of terms, see list of terms relating to algorithms and data structures. For a comparison of running times for a subset of this list see comparison of data structures.
Let ∇ be a connection on the tangent space TN of a smooth manifold N. For smooth mappings h:M→TN from any smooth manifold M, the connector K:TTN→TN satisfies : ∇ h = K Th:TM→TN where Th:TM→TTN is the differential of h.
In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner. Viewed infinitesimally, a connection is a way of differentiating geometric data in such a manner that the derivative is also geometrically meaningful.