A generalized Weyl structure with arbitrary non-metricity

Understand

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.