Projective transformations in metric-affine and Weylian geometries
Dario Sauro, Riccardo Martini, Omar Zanusso
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.
Topics & Concepts
Torsion (gastropod)Pure mathematicsMathematicsAffine transformationConformal mapProjective testAffine geometryCross-ratioGauge theoryConformal geometryRiemann hypothesisMathematical analysisConformal symmetryMathematical physicsAffine spaceSurgeryMedicineCosmology and Gravitation TheoriesAdvanced Differential Geometry ResearchRelativity and Gravitational Theory