  Weyl’s definition says that a change in the affine structure of the manifold \(M\) preserves the projective structure \(\Pi\) of \(M\) if the vectors \(v^{i}_{q}\) and \(\overline{v}^{i}_{q}\) at \(q\) that result from the vector \(v^{i}_{p}\) at \(p\) by parallel transport under \(\Gamma\) and \(\overline{\Gamma}\) respectively, differ at most in length but not in  direction.[41] 