四维可解李群上左不变度量的分类

IF 0.7 Q4 MECHANICS
T. Šukilović
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引用次数: 2

摘要

本文给出了可解李群上任意签名左不变度量的完全分类。用相应李群上的左不变向量场的代数来识别李代数?,内积?? ??on g = Lie g唯一地扩展到一个左不变度规??在李群里。因此,分类问题被简化为被称为度量李代数的对(g, ??,??)的分类问题。尽管两个度量代数可以是等距的,即使对应的李代数是非同构的,但本文将证明在四维可解的情况下,等距意味着同构。最后,考虑了所得到的度量代数的曲率性质,并作为推论,给出了平面、局部对称、Ricciflat、Ricci-parallel和Einstein度量的分类。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Classification of left invariant metrics on 4-dimensional solvable Lie groups
In this paper the complete classification of left invariant metrics of arbitrary signature on solvable Lie groups is given. By identifying the Lie algebra with the algebra of left invariant vector fields on the corresponding Lie group ??, the inner product ??,?? on g = Lie G extends uniquely to a left invariant metric ?? on the Lie group. Therefore, the classification problem is reduced to the problem of classification of pairs (g, ??,??) known as the metric Lie algebras. Although two metric algebras may be isometric even if the corresponding Lie algebras are non-isomorphic, this paper will show that in the 4-dimensional solvable case isometric means isomorphic. Finally, the curvature properties of the obtained metric algebras are considered and, as a corollary, the classification of flat, locally symmetric, Ricciflat, Ricci-parallel and Einstein metrics is also given.
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
4
审稿时长
32 weeks
期刊介绍: Theoretical and Applied Mechanics (TAM) invites submission of original scholarly work in all fields of theoretical and applied mechanics. TAM features selected high quality research articles that represent the broad spectrum of interest in mechanics.
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