THE HOROFUNCTION BOUNDARY OF THE HEISENBERG GROUP: THE CARNOT-CARATHEODORY METRIC

被引：6

作者：

Klein, Tom ^{[1
]}

Nicas, Andrew ^{[2
]}

机构：

[1] 325 Isl Dr,Apt 6, Madison, WI 53705 USA

[2] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4K1, Canada

来源：

CONFORMAL GEOMETRY AND DYNAMICS | 2010年 / 14卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Heisenberg group; Carnot-Caratheodory distance; horofunction boundary; Busemann points; isometries;

D O I：

10.1090/S1088-4173-2010-00217-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We find the horofunction boundary of the (2n + 1)-dimensional Heisenberg group with the Carnot-Caratheodory distance and show that it is homeomorphic to a 2n-dimensional disk and that the Busemann points correspond to the (2n-1)-sphere boundary of this disk. We also show that the compactified Heisenberg group is homeomorphic to a (2n + 1)-dimensional sphere. As an application, we find the group of isometries of the Carnot-Caratheodory distance.

引用

页码：269 / 295

页数：27

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