On the role of the Weyl tensor within the framework of Einstein-Cartan's theory

Abstract It is shown explicitly within a purely world framework that any formal Weyl-like tensor in a curved spacetime which occurs in the realm of Einstein-Cartan's theory may never vanish identically. This property reinstates a result obtained earlier in connection with the derivation of a two-component spinor expression for such a tensor, whereby it is not possible to attain in a spacetime endowed with a torsionful affinity any general condition for conformal flatness that might resemble in form the classical one of general relativity. Some elementary features of the existing torsional cosmological models are likewise brought forward.