Journal of Mathematics of Kyoto University

The ideal boundary of the Sol group

Sungwoon Kim

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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

Permanent link to this document
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
Primary: 53C22: Geodesics [See also 58E10]
Secondary: 57M50: Geometric structures on low-dimensional manifolds

Citation

Kim, Sungwoon. The ideal boundary of the Sol group. J. Math. Kyoto Univ. 45 (2005), no. 2, 257--263. doi:10.1215/kjm/1250281989. https://projecteuclid.org/euclid.kjm/1250281989


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