Classification of left-invariant Einstein metrics on \(\textrm{SL}(2,\mathbb {R})\times \textrm{SL}(2,\mathbb {R})\) that are bi-invariant under a one-parameter subgroup

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2023-03-02 DOI:10.1007/s10455-023-09890-4

Vicente Cortés, Jeremias Ehlert, Alexander S. Haupt, David Lindemann

引用次数: 0

Abstract

We classify all left-invariant pseudo-Riemannian Einstein metrics on \(\textrm{SL}(2,\mathbb {R})\times \textrm{SL}(2,\mathbb {R})\) that are bi-invariant under a one-parameter subgroup. We find that there are precisely two such metrics up to homothety, the Killing form and a nearly pseudo-Kähler metric.

查看原文本刊更多论文

单参数子群下双不变的\（\textrm｛SL｝（2，\mathbb｛R｝）\times\\textrm{SL｝

我们对\（\textrm｛SL｝（2，\mathbb｛R｝）\times\textrm｛SL}（2，/mathbb｛｛R}）\）上的所有左不变伪黎曼-爱因斯坦度量进行了分类，这些度量在单参数子群下是双不变的。我们发现，正是有两个这样的度量，直到同伦论，Killing形式和一个几乎伪Kähler度量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.