Transformation law for Christoffel symbol of first kind

  1. Hi,
    I have met a problem, that is how to prove transformation law for Christoffel symbol of first kind. I have read books about that, but many of them just state: cyclic permutation of the 3 indices and substitution. When I tried to work out, I could not elimate some terms...
    Can anyone show me how to prove it once.
    Will.
     
  2. jcsd
  3. dextercioby

    dextercioby 12,293
    Science Advisor
    Homework Helper

    By prove,u mean calculate it,right??I'll give u the results and the calculations for the second kind symbols and let u strive to find the first kind symbols.
     

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  4. Thx dextercioby,
    I think ,what I have read, is a old style Tensor. So most books, I have read, derive the second kind transformation law from the first kind. Thank you very much for your help. It would be more happy to me if I can get some derives base on the style, what I am learning.

    Will.
     
  5. dextercioby

    dextercioby 12,293
    Science Advisor
    Homework Helper

    No,what u've read was a about 90% of a page from a pdf-format book on GR.That's why it used Greek suffixes.If it's old style,well,i doubt it,since he takes diff.geometry from zero,from the definiton of a topological space.
    I beleive u can manipulate suffices,derivatives and other tensorial quantities so that u can get the first kind symbols' transformation law directly from the expression of a covariant derivative of a covector.

    Daniel.
     
  6. thanks .
     
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