Classification of generalized Einstein metrics on three-dimensional Lie groups

IF 0.6 3区 数学 Q3 MATHEMATICS
V. Cort'es, David Krusche
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引用次数: 2

Abstract

Abstract We develop the theory of left-invariant generalized pseudo-Riemannian metrics on Lie groups. Such a metric accompanied by a choice of left-invariant divergence operator gives rise to a Ricci curvature tensor, and we study the corresponding Einstein equation. We compute the Ricci tensor in terms of the tensors (on the sum of the Lie algebra and its dual) encoding the Courant algebroid structure, the generalized metric, and the divergence operator. The resulting expression is polynomial and homogeneous of degree 2 in the coefficients of the Dorfman bracket and the divergence operator with respect to a left-invariant orthonormal basis for the generalized metric. We determine all generalized Einstein metrics on three-dimensional Lie groups.
三维李群上广义爱因斯坦度量的分类
摘要建立了李群上的左不变广义伪黎曼度量理论。这样的度规伴随着左不变散度算子的选择产生了里奇曲率张量,并研究了相应的爱因斯坦方程。我们根据编码Courant代数结构、广义度量和散度算子的张量(在李代数及其对偶的和上)计算Ricci张量。得到的表达式在广义度量的左不变正交基的Dorfman括号和散度算子的系数中是多项式和2次齐次的。我们确定了三维李群上的所有广义爱因斯坦度量。
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来源期刊
CiteScore
1.80
自引率
0.00%
发文量
58
审稿时长
4.5 months
期刊介绍: The Canadian Journal of Mathematics (CJM) publishes original, high-quality research papers in all branches of mathematics. The Journal is a flagship publication of the Canadian Mathematical Society and has been published continuously since 1949. New research papers are published continuously online and collated into print issues six times each year. To be submitted to the Journal, papers should be at least 18 pages long and may be written in English or in French. Shorter papers should be submitted to the Canadian Mathematical Bulletin. Le Journal canadien de mathématiques (JCM) publie des articles de recherche innovants de grande qualité dans toutes les branches des mathématiques. Publication phare de la Société mathématique du Canada, il est publié en continu depuis 1949. En ligne, la revue propose constamment de nouveaux articles de recherche, puis les réunit dans des numéros imprimés six fois par année. Les textes présentés au JCM doivent compter au moins 18 pages et être rédigés en anglais ou en français. C’est le Bulletin canadien de mathématiques qui reçoit les articles plus courts.
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