## Journal of Mathematics of Kyoto University

### The ideal boundary of the Sol group

Sungwoon Kim

#### Abstract

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

#### Article information

Source
J. Math. Kyoto Univ., Volume 45, Number 2 (2005), 257-263.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250281989

Digital Object Identifier
doi:10.1215/kjm/1250281989

Mathematical Reviews number (MathSciNet)
MR2161691

Zentralblatt MATH identifier
1174.53320

Subjects