On extensions of sub-Riemannian structures on Lie groups

被引：2

作者：

Biggs, Rory ^{[1
]}

Nagy, Peter T. ^{[2
]}

机构：

[1] Rhodes Univ, Dept Math, ZA-6140 Grahamstown, South Africa

[2] Obuda Univ, Inst Appl Math, Becsi Ut 96-b, H-1034 Budapest, Hungary

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2016年 / 46卷

基金：

新加坡国家研究基金会;

关键词：

Sub-Riemannian geometry; Lie groups; Geodesics; METRICS; MOTIONS;

D O I：

10.1016/j.difgeo.2016.02.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define the extension of a left-invariant sub-Riemannian structure in terms of an extension of the underlying Lie group and compatibility of the respective distributions and metrics. We show that geodesics of a structure can be lifted to geodesics of any extension of the structure. In the case of central extensions, we show that the normal geodesics of the minimal extension are the projection (in a sense) of the normal geodesics of any other compatible extension. Several illustrative examples are discussed. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：25 / 38

页数：14

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