Projective transformations in metric-affine and Weylian geometries

We discuss generalizations of the notions of projective transformations acting on affine model of Riemann-Cartan and Riemann-Cartan-Weyl gravity which preserve the projective structure of the light-cones. We show how the invariance under some projective transformations can be used to recast a Riemann-Cartan-Weyl geometry either as a model in which the role of the Weyl gauge potential is played by the torsion vector, which we call torsion-gauging, or as a model with traditional Weyl (conformal) invariance.

Automated summary

We discuss generalizations of projective transformations in the affine model of Riemann-Cartan and Riemann-Cartan-Weyl gravity, which preserve the projective structure of light-cones. We demonstrate how the invariance under certain projective transformations can be utilized to reformulate a Riemann-Cartan-Weyl geometry either as a model with torsion-gauging, where the role of Weyl gauge potential is played by the torsion vector, or as a model with traditional Weyl (conformal) invariance.