  is characteristic of a Riemannian geometry. That geometry requires of the symmetric linear connection \(\Gamma\) that the infinitesimal  parallel transport of a vector always preserves the length of the  vector. Therefore, the metric field in Riemannian geometry determines a unique symmetric linear connection, a “metric  connection” that satisfies the length-preserving condition of  parallel transport. This means that the metric field, locally  represented by (8), is invariant under parallel transport. The  coefficients of this unique symmetric linear metric  connection are given by 