Christoffel Symbol

The Christoffel symbol of a quadratic differential form

is a symbol for the abbreviated representation of the expression

The symbol Γ_{k, ij} is called the Christoffel symbol of the first kind in contrast to the Christoffel symbol of the second kind which is defined by the relation

where g^kt is determined from the equalities

The symbols were introduced by E. Christofl’el in 1869.