Christoffel Symbol of the First Kind

The first type of tensor-like object derived from a Riemannian metric g which is used to study the geometry of the metric. Christoffel symbols of the first kind are variously denoted [ij,k], [i  j; k], Gamma_(abc), or {ab,c}. They are also known as connections coefficients (Misner et al. 1973, p. 210).

The Christoffel symbol of the first kind is defined by


where g_(mk) is the metric tensor, Gamma_(ij)^m is a Christoffel symbol of the second kind, and






See also

Christoffel Symbol, Christoffel Symbol of the Second Kind

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Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 160-167, 1985.Misner, C. W.; Thorne, K. S.; and Wheeler, J. A. Gravitation. San Francisco, CA: W. H. Freeman, 1973.

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Christoffel Symbol of the First Kind

Cite this as:

Weisstein, Eric W. "Christoffel Symbol of the First Kind." From MathWorld--A Wolfram Web Resource.

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