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Lie derivative with respect to anything else

  1. Oct 13, 2011 #1

    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" ?

  2. jcsd
  3. Oct 14, 2011 #2
    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 component-wise lie derivatives. Such a quantity could be another tensor.
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