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

页码：419 / 436

页数：18

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