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Math Help - The Chrystoffel Symbols

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    The Chrystoffel Symbols

    Hi guys. Can someone explain to me what is the geometrical meaning of the Crystoffel symbols. I've tried wikipedia but to no avail.

    P.S.
    By Christoffel symbols I mean \Gamma^\lambda_{\phantom{\lambda} \mu \nu} = \dfrac{1}{2}g^{\lambda \sigma}(g_{\sigma \mu ,\nu} + g_{\sigma \nu ,\mu} - g_{\mu \nu ,\sigma})
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    Quote Originally Posted by fobos3 View Post
    Hi guys. Can someone explain to me what is the geometrical meaning of the Crystoffel symbols. I've tried wikipedia but to no avail.

    P.S.
    By Christoffel symbols I mean \Gamma^\lambda_{\phantom{\lambda} \mu \nu} = \dfrac{1}{2}g^{\lambda \sigma}(g_{\sigma \mu ,\nu} + g_{\sigma \nu ,\mu} - g_{\mu \nu ,\sigma})
    The "covariant derivative" of a vector A_k, A_{m;n} is the ordinary derivative minus \Gamma^k_{mn} A_k and so that last term essentially measures how much the change in a function is due to the coordinate system rather than the function. By the way, since the "ordinary derivative" is not a tensor, neither are the Christoffel symbols which is why some people prefer the notation \left[\begin{array}{c}k \\ mn\end{array}\right] since it doesn't "look" so much like a tensor.
    Last edited by mr fantastic; February 14th 2009 at 01:11 PM. Reason: Fixed some latex
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