covariant | semicolon derivative

The covariant derivative of a contravariant tensor A^a (also called the "semicolon derivative" since its symbol is a semicolon) is given by A^a_(;b) | = | (dA^a)/(dx^b) + Γ_(b k)^a A^k | = | A^a_(, b) + Γ_(b k)^a A^k (Weinberg 1972, p. 103), where Γ_(i j)^k is a Christoffel symbol, Einstein summation has been used in the last term, and A_(, k)^k is a comma derivative. The notation del ·A, which is a generalization of the symbol commonly used to denote the divergence of a vector function in three dimensions, is sometimes also used.

Christoffel symbol | comma derivative | covariant tensor | divergence | Levi-Civita connection