The horofunction boundary of the Heisenberg group

Tom Klein and Andrew Nicas

Vol. 242 (2009), No. 2, 299–310

DOI: 10.2140/pjm.2009.242.299

Abstract

We find the horofunction boundary of the (2n + 1)-dimensional Heisenberg group with the Korányi metric and show that it is homeomorphic to a 2n-dimensional disk. We also show that the Busemann points correspond to the (2n− 1)-sphere boundary of this disk. We show that the compactified Heisenberg group is homeomorphic to a (2n + 1)-dimensional sphere.

Keywords

Heisenberg group, Korányi metric, horofunction boundary, Busemann points

Mathematical Subject Classification 2000

Primary: 20F65, 22E25, 53C23

Secondary: 53C70

Milestones

Received: 10 December 2008

Revised: 15 April 2009

Accepted: 1 May 2009

Published: 1 October 2009