The signature of the Ricci curvature of left invariant Riemannian   metrics on 4-dimensional Lie groups
  In this paper, we present the classification of all possible signatures of the Ricci curvature of left-invariant Riemannian metrics on 4-dimensional Lie groups and discuss some related questions. 
A.G. Kremlyov (Rubtsovsk Industrial Institute), Yu.G. Nikonorov (South   Mathematical Institute of V.S.C. RAS)