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
Hoverbike drone project for air transport takes off
Earlier Stone Age artifacts found in Northern Cape of South Africa
Study reveals new characteristics of complex oxide surfaces
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