KILLING'S EQUATIONS FOR INVARIANT METRICS ON LIE GROUPS

被引：2

作者：

Hindeleh, Firas ^{[1
]}

Thompson, Gerard ^{[2
]}

机构：

[1] Grand Valley State Univ, Allendale, MI 49401 USA

[2] Univ Toledo, Toledo, OH 43606 USA

来源：

JOURNAL OF GEOMETRIC MECHANICS | 2011年 / 3卷 / 03期

关键词：

Lie algebra; Lie group; right-invariant Riemannian metric; Killing vector field;

D O I：

10.3934/jgm.2011.3.323

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article is the first in a series that will investigate symmetry and curvature properties of a right-invariant metric on a Lie group. This paper will consider Lie groups in dimension two and three and will focus on the solutions of Killing's equations. A striking result is that several of the three-dimensional Lie groups turn out to be spaces of constant curvature.

引用

页码：323 / 335

页数：13

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