Lie groups as 4-dimensional Riemannian or pseudo-Riemannian almost   product manifolds with nonintegrable structure
  A Lie group as a 4-dimensional pseudo-Riemannian manifold is considered. This manifold is equipped with an almost product structure and a Killing metric in two ways. In the first case Riemannian almost product manifold with nonintegrable structure is obtained, and in the second case - a pseudo-Riemannian one. Each belongs to a 4-parametric family of manifolds, which are characterized geometrically. 
Dimitar Mekerov