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

$\nabla_{\dot\gamma(t)}V=0$

for any t.

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Parallel transport

See also: Parallel transport, Connection (mathematics), Covariant derivative, Curve, Manifold, Mathematics