半简单弱对称伪黎曼流形

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-08-29 DOI:10.1007/s12188-018-0195-8

Zhiqi Chen, Joseph A. Wolf

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引用次数: 5

摘要

我们发展了弱对称伪黎曼流形G/H的分类，其中G是半单李群，H是约化子群。我们从G是紧致的情况导出了分类，然后讨论了H在G/H的切空间上的（各向同性）表示和不变伪黎曼度量的特征。因此，我们得到了洛伦兹签名（（n-1,1））和反洛伦兹签名的半单弱对称流形（（n-2,2））的分类。

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Semisimple weakly symmetric pseudo-Riemannian manifolds

We develop the classification of weakly symmetric pseudo-Riemannian manifolds G / H where G is a semisimple Lie group and H is a reductive subgroup. We derive the classification from the cases where G is compact, and then we discuss the (isotropy) representation of H on the tangent space of G / H and the signature of the invariant pseudo-Riemannian metric. As a consequence we obtain the classification of semisimple weakly symmetric manifolds of Lorentz signature \((n-1,1)\) and trans-Lorentzian signature \((n-2,2)\).

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来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.