### Sol Geometry

Sol is one of the eight homogeneous geometries relevant to Geometrization in dimension three, given by $\mathbb{R}^3$ together with the metric $ds^2=e^{2z}dx^2+e^{-2z}dy^2+dz^2$.

Sol is one of the eight homogeneous geometries relevant to Geometrization in dimension three, given by $\mathbb{R}^3$ together with the metric $ds^2=e^{2z}dx^2+e^{-2z}dy^2+dz^2$.