Parallel transport
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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 <math>V<math> on a smooth curve <math>\gamma<math> is called parallel if
- <math>\nabla_{\dot\gamma(t)}V=0<math>
for any t.
See also: Connection (mathematics), Covariant derivative