A restriction on proper actions on homogeneous spaces of reductive type
  Let L be a reductive subgroup of a reductive Lie group G. Let G/H be a homogeneous space of reductive type. We provide a necessary condition for the properness of the action of L on G/H. As an application we give examples of spaces that do not admit standard compact Clifford-Klein forms. 
Maciej Bochenski, Marek Ogryzek
math.GR