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Encyclopedia > Parallel transport

In mathematics, a parallel transport on a manifold M with specified connection is a way to transport vectors along smooth curves, in such a way that they stay "parallel" with respect to the given connection. A field V on a smooth curve γ is called parallel if Mathematics is the study of quantity, structure, space and change. ... In mathematics, a differentiable manifold is a topological space that looks locally like the Euclidean space Rn, and the Euclidean space indeed provides the simplest example of a manifold. ... In differential geometry, a connection (also connexion) or covariant derivative is a way of specifying a derivative of a vector field along another vector field on a manifold. ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ...

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Parallel - Wikipedia, the free encyclopedia (249 words)
Parallel computing is the simultaneous execution of the same task (split up and specially adapted) on multiple processors in order to obtain faster results.
In electronics, components are said to be "in parallel" if current branches to flow through both simultaneously, as against "in series" where the current flows through first one, then the other, along a single path.
Parallel trenches in siege warfare are the trenches dug by besiegers in a generally parallel direction to the front of a stronghold chosen for attack.
Parallel transport - definition of Parallel transport in Encyclopedia (92 words)
Parallel transport - definition of Parallel transport in Encyclopedia
In mathematics, a parallel transport on a manifold M with specified connection is a way to transport vectors along smooth curves, in such a way that they stay "parallel" with respect to the given connection.
A field V on a smooth curve γ is called parallel if
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