New Explicit Lorentzian Einstein-Weyl Structures in 3-Dimensions

Joël Merker, Paweł Nurowski

On a $3$D manifold, a Weyl geometry consists of pairs $(g,A)=$ (metric, $1$-form) modulo gauge $\hat{g}={\mathrm{e}}^{2\phi }g$, $\hat{A}=A+\mathrm{d}\phi$. In 1943, Cartan showe…