Related papers: Geometry from geodesics: fine-tuning Ehlers, Piran…

A new 8-dim conformal gauging solves the auxiliary field problem and eliminates unphysical size change from Weyl's electromagnetic theory. We derive the Maurer-Cartan structure equations and find the zero curvature solutions for the…

In a previous paper, we presented new results on non-Riemannian geometry. For an asymmetric connection, we showed that a projective change in the symmetric part generates a vector field that is not arbitrary, but is the gradient of a…

Weyl's conformal theory of gravity is an extension of Einstein's theory of general relativity which associates metrics with 1-forms . In the case of locally integrable (closed non-exact) 1-forms the spacetime manifolds are no more simply…

We develop the properties of Weyl geometry, beginning with a review of the conformal properties of Riemannian spacetimes. Decomposition of the Riemann curvature into trace and traceless parts allows an easy proof that the Weyl curvature…

In view of Ehlers-Pirani-Schild formalism, since 1972 Weyl geometries should be considered to be the most appropriate and complete framework to represent (relativistic) gravitational fields. We shall here show that in any given Lorentzian…

We revisit Weyl's metrication (geometrization) of electromagnetism. We show that by making Weyl's proposed geometric connection be pure imaginary, not only are we able to metricate electromagnetism, an underlying local conformal invariance…

We discuss the concepts of Weyl and Riemann frames in the context of metric theories of gravity and state the fact that they are completely equivalent as far as geodesic motion is concerned. We apply this result to conformally flat…

We review (non-supersymmetric) gauge theories of four-dimensional space-time symmetries and their quadratic action. The only true gauge theory of such a symmetry (with a physical gauge boson) that has an exact geometric interpretation,…

The quotient of the conformal group of Euclidean 4-space by its Weyl subgroup results in a geometry possessing many of the properties of relativistic phase space, including both a natural symplectic form and non-degenerate Killing metric.…

The (4+1) dimensional conformally flat Eisenhart geometry is investigated in this work, stressing the contribution of the stress tensor generating its curvature. The energy-momentum tensor $T^{a}_{~b}$ is traceless and has only one nonzero…

We show that on a surface locally every affine torsion-free connection is projectively equivalent to a Weyl connection. First, this is done using exterior differential system theory. Second, this is done by showing that the solutions of the…

Using a combination of techniques from conformal and complex geometry, we show the potentialization of 4-dimensional closed Einstein-Weyl structures which are half-algebraically special and admit a "half-integrable" almost-complex…

Consistency of Weyl natural gauge, Lorentz gauge and nonlinear gauge is studied in Weyl geometry. Field equations in generalized Weyl-Dirac theory show that spinless electron and photon are topological defects. Statistical metric and…

I state and prove, in the context of a space having only the metrical and affine structure imposed by the geometrized version of Newtonian gravitational theory, a theorem analagous to that of Weyl's for a Lorentz manifold. The theorem says…

We review recent developments in physical implications of Weyl conformal geometry. The associated Weyl quadratic gravity action is a gauge theory of the Weyl group of dilatations and Poincar\'e symmetry. Weyl conformal geometry is defined…

One of the important extensions of Riemann geometry is Weyl geometry, which is essentially based on the ideas of conformal invariance and nonmetricity. A similar non-Riemannian geometry was proposed by Erwin Schr\"{o}dinger in the late…

We investigate the geometry of a twisting non-shearing congruence of null geodesics on a conformal manifold of even dimension greater than four and Lorentzian signature. We give a necessary and sufficient condition on the Weyl tensor for…

We explicitly prove that the Weyl conformal symmetry solves the black hole singularity problem, otherwise unavoidable in a generally covariant local or non-local gravitational theory. Moreover, we yield explicit examples of local and…

We investigate the coupling of matter to geometry in conformal quadratic Weyl gravity, by assuming a coupling term of the form $L_m\tilde{R}^2$, where $L_m$ is the ordinary matter Lagrangian, and $\tilde{R}$ is the Weyl scalar. The coupling…

In the literature different concepts of compatibility between a projective structure and a conformal structure on a differentiable manifold are used. In particular compatibility in the sense of Weyl geometry is slightly more general than…