(The) ideal boundary of Sol

Abstract

We obtain equations of geodesic lines in the Lie group $\mathbf{Sol}$ and prove that the ideal boundary of the $\mathbf{Sol}$ is a set $\mathcal{R}=\{(x,y,z)| xy=0, and x^2+y^2+z^2=1\}$ with a degenerate Tits metric i.e., the distance between different points equals ∞.