 All these transformations leave invariant the three independent differentials ("dx", "dy", "dz") from which the line element is constructed.In the general case of a non-Euclidean homogeneous space, the transformations of its group of motions again leave invariant three independent linear differential forms, which do not, however, reduce to total differentials of any coordinate functions.These forms are written as formula_3 where the Latin index ("a") labels three independent vectors (coordinate functions); these vectors are called a frame field or triad.