Christoffel symbols


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Christoffel symbols

[′kris·tȯf·əl ‚sim·bəlz]
(mathematics)
Symbols that represent particular functions of the coefficients and their first-order derivatives of a quadratic form. Also known as three-index symbols.
References in periodicals archive ?
The components of the corresponding metric tensor h and the Christoffel symbols on the manifold N will be denoted by [h.
Now, an alternative (although implicit) definition of the Christoffel symbols is contained in the equation that states the vanishing of covariant derivatives of the metric:
This theory has some advantages over the general relativity; the quantities such as christoffel symbols and others become tensors which otherwise in Riemannian geometry they are not.
One straightforwardly goes through the tedious calculation of the Christoffel symbols and the components of the Ricci tensor, finding:
n], n > k this leads to the Ricci tensor R, in components [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are Christoffel symbols.
n]) is a coordinate chart on M, then the Christoffel symbols [[GAMMA].
v[lambda] are the Christoffel symbols of the second kind, and [S.
CHRISTOFFEL SYMBOLS OF PSEUDO-RIEMANNIAN MANIFOLD (M,h), h = [[nabla]sup.
We recall that the Christoffel symbols of second kind related to a given [THETA](4)-invariant spacetime metric [3] are the components of a [THETA](4)-invariant tensor field and depend on ten functions [B.
as the Christoffel symbols (symmetric in their two lower indices) and
which are just the Christoffel symbols {[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]} in the space-time [S.