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Lie derivative with respect to anything else 
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#1
Oct1311, 07:59 PM

P: 647

Hi,
I have been looking around, and I can't seem to find a slightly different version of the lie derivative where the lie derivative is taken with respect to a tensor field, rather than a vector field. That is, a quantity which measures the change in a vector field, along the "flow" of a tensor field. I am not asking about the lie derivative of a tensor, which is the change in a tensor field through the flow of a vector field. does such a derivative exist? is this a reasonable question? Also, would a different, but correct way to describe the Lie derivative be "it measures the change in a tensor field with respect to the change in a vector field" ? Thanks, 


#2
Oct1411, 08:04 AM

P: 336

I can't think of a definition of the lie derivative with respect to a covector off my head.
However, we may talk about the lie derivative with respect to a totally contravariant tensor.We could define it as the tensor product of componentwise lie derivatives. Such a quantity could be another tensor. 


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