Register to reply

Lie derivative with respect to anything else

by jfy4
Tags: derivative, respect
Share this thread:
jfy4
#1
Oct13-11, 07:59 PM
jfy4's Avatar
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,
Phys.Org News Partner Science news on Phys.org
Sapphire talk enlivens guesswork over iPhone 6
Geneticists offer clues to better rice, tomato crops
UConn makes 3-D copies of antique instrument parts
Eynstone
#2
Oct14-11, 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 component-wise lie derivatives. Such a quantity could be another tensor.


Register to reply

Related Discussions
Derivative of e^(x^x) with respect to x Calculus & Beyond Homework 5
Derivative with respect to... General Math 12
Derivative of g(h(t), t) with respect to h Calculus 4
Derivative with respect to something else Calculus 5
Derivative of U(X(t),t) with respect to t Calculus 1