Left-invariant pseudo-Riemannian metrics on four-dimensional Lie groups   with zero Schouten-Weyl tensor
  In the presented paper left-invariant pseudo-Riemannian metrics on four-dimensional Lie groups with zero Schouten-Weyl tensor are investigated. The complete classification of these metric Lie groups is obtained in terms of the structure constants of corresponding Lie algebras. 
Olesya P. Khromova, Pavel N. Klepikov, Eugene D. Rodionov
math.DG