Classification of left-invariant Einstein metrics on SL(2, R) x SL(2, R) that are bi-invariant under a one-parameter subgroup

被引：0

作者：

Cortes, Vicente ^{[1
,2
]}

Ehlert, Jeremias ^{[1
,2
]}

Haupt, Alexander S. ^{[1
,2
]}

Lindemann, David ^{[3
]}

机构：

[1] Univ Hamburg, Dept Math, Bundesstr 55, D-20146 Hamburg, Germany

[2] Univ Hamburg, Ctr Math Phys, Bundesstr 55, D-20146 Hamburg, Germany

[3] Aarhus Univ, Dept Math, Ny Munkegarde 118, DK-8000 Aarhus C, Denmark

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2023年 / 63卷 / 02期

关键词：

Special linear group; Einstein manifolds; Non-compact homogeneous pseudo-Riemannian manifolds;

D O I：

10.1007/s10455-023-09890-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify all left-invariant pseudo-Riemannian Einstein metrics on SL(2, R) x SL(2, 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-Kahler metric.

引用

页数：16

共 43 条

[1] On naturally reductive left-invariant metrics of SL(2, R)
Halverscheid, Stefan
Iannuzzi, Andrea
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2006, 5 (02) : 171 - 187
[2] Classification of left-invariant Einstein metrics on SL(2,R)×SL(2,R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textrm{SL}(2,\mathbb {R})\times \textrm{SL}(2,\mathbb {R})$$\end{document} that are bi-invariant under a one-parameter subgroup
Vicente Cortés
Jeremias Ehlert
Alexander S. Haupt
David Lindemann
Annals of Global Analysis and Geometry, 2023, 63 (2)
[3] Invariant generalized functions on sl(2,R) with values in a sl(2,R)-module
Lavaud, P
JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 219 (01) : 226 - 244
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DIFFERENTIAL EQUATIONS, 2014, 50 (11) : 1541 - 1547
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Differential Equations, 2014, 50 : 1541 - 1547
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JOURNAL OF HIGH ENERGY PHYSICS, 2007, (02):
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Journal of Mathematical Sciences, 2007, 143 (1) : 2754 - 2764
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JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2008, 15 (Suppl 3) : 362 - 372
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