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Isotropic tensors

  1. Jan 9, 2006 #1
    Hello everyone, this seems like a great forum here with a lot of knowlegable people and I was hoping someone could help me out with this question. I'm an engineering student and I've recently decided to switch into physics. Now I'm trying to catch up on the math I'm going to need, so I'm studying tensors. The book I'm using says
    "It can be shown that the most general isotropic tensor of order four is of the form [tex]\eta_{iklm}=A\delta_{ik}\delta_{lm} + B\delta_{il}\delta_{km} +C\delta_{im}\delta_{kl}[/tex]"
    At the time I read that I just skipped over it because I couldn't figure out how to get that and it didn't seem that important. But later on in the book they have a whole section on fluid mechanics where they use this to derive the Navier-Stokes equations and then from there on everything they do involves these equations, so its very frustrating not to understand this one little equation because it basically means I don't follow the whole section. Could anyone tell me where I could find a proof of this or outline how the proof goes? Thanks a lot!
  2. jcsd
  3. Jan 10, 2006 #2


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    Possibly helpful:
    http://www.ig.utexas.edu/people/students/classes/spring02/geo391/Lecture1.pdf [Broken]
    Last edited by a moderator: May 2, 2017
  4. Jan 10, 2006 #3
    Very helpful. Thank you!
    Last edited by a moderator: May 2, 2017
  5. Sep 29, 2009 #4
    Except that Lecture 1 missed that the permutation tensor is isotropic of rank 3.
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