Projective transformations in metric-affine and Weylian geometries

Abstract

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.

13 pages, published version

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Cited by in corpus (4)

• Radiative corrections to the $R$ and $R^2$ invariants from torsion fluctuations on maximally symmetric spaces
• On the geometric origin of the energy-momentum tensor improvement terms
• Heat kernel of non-minimal second-order operators
• Gravitational waves in Palatini gravity for a non-minimal geometry-matter coupling