The Christoffel symbol of the first kind is the non-tensorial quantity obtained from the Christoffel symbol of the second kind by lowering its upper index with the metric:Ĭ lij = g kl C ij k = 1 2 g il, j + g jl, i − g ij, l , ![]() Where g ij and g ij are the components of the metric and its inverse, respectively, and where a comma indicates a partial derivative. ![]() It can be represented as a 3-index set of coefficients:Ĭ ij k = 1 2 g kl g il, j + g jl, i − g ij, l , The Christoffel symbol of the second kind for a metric g is the unique torsion-free connection such that the associated covariant derivative operator ∇ satisfies ∇ g = 0. Keyword - (optional) a keyword string, either " FirstKind " or " SecondKind " H - (optional) the inverse of the metric g G - a metric tensor on the tangent bundle of a manifold ![]() Tensor - find the Christoffel symbols of the first or second kind for a metric tensor
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |