## Tsukuba Journal of Mathematics

### A splitting theorem for $CAT(0)$ spaces with the geodesic extension property

Tetsuya Hosaka

#### Abstract

In this paper, we show the following splitting theorem: For a proper $\mathrm{CAT}(0)$ space $X$ with the geodesic extension property, if a group $\Gamma=G_{1}\times G_{2}$ acts geometrically (i.e., properly discontinuously and cocompactly by isometries) on $X$, then $X$ splits as a product $X_{1}\times X_{2}$ and there exist geometric actions of $G_1$ and some subgroup of finite index in $G_2$ on $X_1$ and $X_2$, respectively.

#### Article information

Source
Tsukuba J. Math., Volume 27, Number 2 (2003), 289-293.

Dates
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1496164649

Digital Object Identifier
doi:10.21099/tkbjm/1496164649

Mathematical Reviews number (MathSciNet)
MR2025728

Zentralblatt MATH identifier
1050.20029

#### Citation

Hosaka, Tetsuya. A splitting theorem for $CAT(0)$ spaces with the geodesic extension property. Tsukuba J. Math. 27 (2003), no. 2, 289--293. doi:10.21099/tkbjm/1496164649. https://projecteuclid.org/euclid.tkbjm/1496164649