  However, a conformal structure by itself does not determine a unique  symmetric linear connection; it only determines an equivalence class  of conformally equivalent connections \(K = [\Gamma]\), namely,  connections which preserve the conformal structure \(C\) during  parallel transport. The difference between any two conformally  equivalent symmetric linear connections \(\overline{\Gamma}^{\,i}_{jk}\),  \(\Gamma^i_{jk} \in [\Gamma]\) is given by 