The Parallel transport reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

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 simple smooth curve γ is called parallel if

for any t.

See also: Connection (mathematics), Covariant derivative

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