Homogeneous locally conformally Kaehler and Sasaki manifolds
  We prove various classification results for homogeneous locally conformally symplectic manifolds. In particular, we show that a homogeneous locally conformally Kaehler manifold of a reductive group is of Vaisman type, if the normalizer of the isotropy group is compact. We also show that such a result does not hold in the case of noncompact normalizer and determine all left-invariant locally conformally Kaehler structures on reductive Lie groups. 
Dmitri V. Alekseevsky, Vicente Cortes, Keizo Hasegawa and Yoshinobu   Kamishima
math.DG