Reductive homogeneous Lorentzian manifolds

We study homogeneous Lorentzian manifolds M=G/L of a connected reductive Lie group G modulo subgroup L, under the assumption that M is (almost) G-effective and isotropy representation totally reducible. show description such reduces to case semisimple groups G. Moreover, we prove space reductive. describe all reducible subgroups Lorentz divide them into three types. The Type I are compact, while II III non-compact. explicit corresponding spaces (under some mild assumption) given. also L an admissible manifold, i.e., effective manifold admits invariant metric. Whenever maximal with these properties, call minimal admissible. classify G/L compact metrics on them.