Riemannian manifolds with some restrictions on an integer part of the curvature tensor decomposition as a direct sum of the Kulkarni-Nomizu product of one-dimensional curvature tensor with the metric tensor and the Weyl tensor are investigated in this paper. Besides this we construct some examples of Riemannian metrics with negative Ricci curvature and sign-changing one-dimensional curvature.

Key words: Lie algebras and Lie groups, left-invariant Riemannian metrics, curvature tensor.