# A generalized Weyl structure with arbitrary non-metricity

## TL;DR

This paper generalizes Weyl structures by allowing arbitrary non-metricity and extending symmetry transformations, broadening the mathematical framework of Weyl geometry.

## Contribution

It introduces two new generalizations of Weyl structures: one with arbitrary non-metricity under conformal symmetry, and another with disformal transformations.

## Key findings

- Two new classes of Weyl structures are formulated.
- The generalized structures encompass standard Weyl geometry as special cases.
- Potential applications in modified gravity theories are discussed.

## Abstract

A Weyl structure is usually defined by an equivalence class of pairs $({\bf g}, \boldsymbol{\omega})$ related by Weyl transformations, which preserve the relation $\nabla {\bf g}=\boldsymbol{\omega}\otimes{\bf g}$, where ${\bf g}$ and $\boldsymbol{\omega}$ denote the metric tensor and a 1-form field. An equivalent way of defining such a structure is as an equivalence class of conformally related metrics with a unique affine connection $\Gamma_{\boldsymbol{\omega}}$, which is invariant under Weyl transformations. In a standard Weyl structure, this unique connection is assumed to be torsion-free and have vectorial non-metricity. This second view allows us to present two different generalizations of standard Weyl structures. The first one relies on conformal symmetry while allowing for a general non-metricity tensor, and the other comes from extending the symmetry to arbitrary (disformal) transformations of the metric.