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Christoffel symbols examples

  1. Mar 20, 2007 #1
    i'm having a hard time computing these so could people show me several examples to help me get a better feel for them before I move on to curvature?
  2. jcsd
  3. Mar 20, 2007 #2


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    One of the simplest examples would be to calculate the connection coefficients for the 3D Euclidean space using spherical polar coordinates. Here the line element is of the form [tex]ds^2=dr^2+r^2d\theta^2+r^2\sin^2\theta d\phi^2[/tex]. Could you try this one?

    As an aside, have you studied and Lagrangian mechanics? If so, there is a method of obtaining the connection coefficients from the Euler-Lagrange equations which is sometimes less time consuming than using the definition involving the metric tensor.
  4. Mar 20, 2007 #3
    No but i know the euler lagrage equation.
  5. Mar 20, 2007 #4


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    Maybe it's easier to just use the definition of the symbols. Try plugging in the metric coefficients and see what you get for the gammas.
  6. Mar 20, 2007 #5
    Yes but could you still show me some examples, i'm not particularly comfortable with thses symbols.
  7. Mar 20, 2007 #6


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  8. Mar 20, 2007 #7
    It's ok I'm fine now.
  9. Mar 24, 2007 #8
    If you have Maple and GRTensor package you can calculate christoffel symbols for many metric files coming with the grtensor package and work them out yourself to exercise.
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