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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.
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