Many mathematicians devoted their papers to the investigation of the relationship between various curvature types and the topology of the Riemannian manifolds [1-4]. An influence of the Ricci curvature and one- dimensional curvature on the topology of the homogeneous Riemannian manifolds was studied in [2-4]. In this paper the sign-defined Ricci and one-dimensional curvatures domains were studied for the case of three-dimensional Lie groups with left-invariant Riemannian metrics.

Key words: Lie groups and Lie algebras, left-invariant Riemannian metrics, Ricci curvature, one-dimensional curvature operator.