 Pseudo-Riemannian Metric. Since length transfer is  non-integrable (i.e., path-dependent) in a Weyl space, a Weyl  geometry reduces to a pseudo-Riemannian geometry if and only if  Weyl’s length-curvature  (Streckenkrümmung) tensor equals  zero, in which case the length of a vector is path-independent under  parallel transport, and there exists no second clock effect.