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Homework Help: Covariant derivative of the Christoffel symbol

  1. Jul 25, 2010 #1
    1. The problem statement, all variables and given/known data
    Is the covariant derivative of a Christoffel symbol equal to zero? It seems like it would be since it is composed of nothing but metrics, and the covariant derivative of any metric is zero, right?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 25, 2010 #2

    nicksauce

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    This seems like a meaningless question. The covariant derivative acts on tensors, but the Christoffel symbols are not tensors.
     
  4. Jul 25, 2010 #3
    That's the first thing that came to my mind, but then the covariant derivative can still act on all the terms of the Christoffel symbol, since it is composed of tensors, so it seemed like it might still be a meaningful question. With that in mind, would you still consider it to be meaningless?
     
  5. Jul 26, 2010 #4

    nicksauce

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    You mean because it is built out of metrics? But it is built out of partial derivatives of metrics, which makes the terms no longer tensors.
     
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