Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reductive homogeneous Lorentzian manifolds   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.

29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
18
The categories of this paper are: econ