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- Thread starter latentcorpse
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fzero

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[tex] D ( v \otimes w ) = (Dv)\otimes w + v \otimes (Dw).[/tex]

Therefore the part that you proved above follows. Now, since [tex]l^2[/tex] is a scalar, it's covariant derivative reduces to the ordinary derivative. You can see this by explicit computation, since the signs in front of the Christoffel symbols are opposite when acting on covariant and contravariant vectors.

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