Parallel Transport
In general, parallel transport along a curve with respect to a connection defines isomorphisms between the tangent spaces at the points of the curve. If the connection is a Levi-Civita connection, then these isomorphisms are orthogonal – that is, they preserve the inner products on the various tangent spaces.
Read more about this topic: Levi-Civita Connection
Famous quotes containing the words parallel and/or transport:
“There is a parallel between the twos and the tens. Tens are trying to test their abilities again, sizing up and experimenting to discover how to fit in. They don’t mean everything they do and say. They are just testing. . . . Take a good deal of your daughter’s behavior with a grain of salt. Try to handle the really outrageous as matter-of-factly as you would a mistake in grammar or spelling.”
—Stella Chess (20th century)
“One may disavow and disclaim vices that surprise us, and whereto our passions transport us; but those which by long habits are rooted in a strong and ... powerful will are not subject to contradiction. Repentance is but a denying of our will, and an opposition of our fantasies.”
—Michel de Montaigne (1533–1592)