On a Completely Antisymmetric Cartan Tensor

Theory of General Relativity is considered from the point of view of its general structure; it has been showed that if one assumes any connection to be a metric connection then Cartan tensor must necessary be completely antisymmetric, and an example of application is considered in the case of Lie group theory. Under a geometrical point of view, Cartan tensor is thought to represent the Torsion of the space; a completely antisymmetric torsion is the superfield which squashes S7, inducing the mechanism of spontaneous compactification of the 11-dimensional space, in multidimensional theories, or in alternative, in 4-dimensional theories, torsion is the reaction of the spacetime to the presence of spin, and modified field equations are presented, as well as possible ways to detect torsion from a cosmological and a microscopical point of view.