论文标题
还原性同质洛伦兹歧管
Reductive homogeneous Lorentzian manifolds
论文作者
论文摘要
我们研究了一个连接的还原谎言组的均质Lorentzian歧管$ M = g/l $ $ g $ modulo a连接的还原亚组$ l $，假设$ m $ IS（几乎）$ g $有效，并且同位素拷贝代表完全还原。我们表明，这种歧管的描述减少到半圣母谎言组$ g $的情况下。此外，我们证明了这种均匀的空间是还原性的。我们描述了Lorentz组的所有完全还原的亚组，并将其分为三种类型。 I型的亚组是紧凑的，而II型和III型的亚组是非紧凑的。对相应的II和III型Lorentzian空间的明确描述（在某些温和的假设下）。我们还表明，Lorentz同质流形的描述$ m = g/l $ i类型，减少了子组$ l $的描述，使得$ m = g/l $是可允许的流形，即，是一种有效的同质歧管，它承认了一个不变的lorentzian lorentzian lorentzian Metric。每当亚组$ l $是具有这些属性的最大子组时，我们都称其为可允许的多方面。我们对紧凑的半圣母谎言组的所有最低允许的同质流形分类$ g/l $ $ g $，并描述所有不变的洛伦兹指标。
We study homogeneous Lorentzian manifolds $M = G/L$ of a connected reductive Lie group $G$ modulo a connected reductive subgroup $L$, under the assumption that $M$ is (almost) $G$-effective and the isotropy representation is totally reducible. We show that the description of such manifolds reduces to the case of semisimple Lie groups $G$. Moreover, we prove that such a homogeneous space is reductive. We describe all totally reducible subgroups of the Lorentz group and divide them into three types. The subgroups of Type I are compact, while the subgroups of Type II and Type III are non-compact. The explicit description of the corresponding homogeneous Lorentzian spaces of Type II and III (under some mild assumption) is given. We also show that the description of Lorentz homogeneous manifolds $M = G/L$ of Type I, reduces to the description of subgroups $L$ such that $M=G/L$ is an admissible manifold, i.e., an effective homogeneous manifold that admits an invariant Lorentzian metric. Whenever the subgroup $L$ is a maximal subgroup with these properties, we call such a manifold minimal admissible. We classify all minimal admissible homogeneous manifolds $G/L$ of a compact semisimple Lie group $G$ and describe all invariant Lorentzian metrics on them.
