A note on flat nonholonomic Riemannian structures on three-dimensional Lie groups

被引：3
|
作者：
Barrett, Dennis, I [1 ]
Remsing, Claudiu C. [1 ]
机构：
[1] Rhodes Univ, Dept Math, ZA-6140 Grahamstown, South Africa
来源：
BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY | 2019年 / 60卷 / 03期
基金：
新加坡国家研究基金会;
关键词：
Nonholonomic Riemannian structure; Nonholonomic connection; Lie group;
D O I：
10.1007/s13366-018-0421-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider flat nonholonomic Riemannian manifolds, i.e., those whose associated parallel transport (induced by the nonholonomic connection) is path-independent. We first characterize flatness for structures on three-dimensional manifolds, and hence classify the flat left-invariant structures on simply connected Lie groups.
引用
收藏
页码：419 / 436
页数：18
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