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Please prove this

  1. Jan 6, 2008 #1
    Hello. I'm learning tensor analysis. I have a problem. We know that

    [tex]\Gamma^i_{jk}=\vec{\epsilon^i}\cdot\frac{\partial\vec{\epsilon_j}}{\partial q^k}[/tex]

    Please prove the relation

    [tex]\frac{\partial\vec{\epsilon_j}}{\partial q^k}=\Gamma^m_{jk}\vec{\epsilon_m}[/tex]

    Thanks very much in advance
    Last edited: Jan 6, 2008
  2. jcsd
  3. Jan 6, 2008 #2
    What'll you pay me?
  4. Jan 21, 2008 #3
  5. Jan 23, 2008 #4
    Thanks hanskuo.

    I knew this proof, but I thought that it is only correct for the inverse relation. I was wrong!
  6. Jan 24, 2008 #5
    you are wellcome, Arham

    Now I'm learning Differential Geometry,too.
    do you begin to lerane covariant derivatives or not ?
  7. Jan 24, 2008 #6
    I'm an undergraduate physics student, hanskuo. I am learning tensor analysis from George Arfken's book. As you know, this book has a brief introduction to Covariant Derivative; I have read it. But I should do more exercises and read more about it in future.
  8. Jan 24, 2008 #7
    There are a lot of things interesting for covariant derivatives.
    your original question likes this:
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