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pervect
#30
Oct17-10, 05:25 AM
Emeritus
Sci Advisor
P: 7,631
Quote Quote by Phrak View Post
hmm. what would be the result of parallel transporting a covariant vector?
Using the abstract approach, you can parallel transport an arbitrary tensor along a curve. If you have some tensor [itex]T^{qwer}{}_{uiop}[/itex] you parallel transport it along a curve with tangent t^a by insisting that along the curve

[itex]t^a \, \nabla_a T^{qwer}{}_{uiop} = 0[/itex]

Though as I said, the intuitive meaning, if any, tends to get lost along the way, at least for me.