Locally conformal flat Riemannian manifolds with constant principal Ricci curvatures and locally conformal flat C-spaces

It is proved that every locally conformal flat Riemannian manifold all of whose Jacobi operators have constant eigenvalues along every geodesic is with constant principal Ricci curvatures. A local classification (up to an isometry) of locally conformal flat Riemannian manifold with constant Ricci eigenvalues is given in dimensions 4, 5, 6, 7 and 8. It is shown that any n-dimensional (4 ≤ n ≤ 8) locally conformal flat Riemannian manifold with constant principal Ricci curvatures is a Riemannian locally symmetric space. Running title: Constant Ricci eigenvalues and C-spaces.