  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
$(4\leq n \leq 8)$ locally conformal flat Riemannian manifold with constant
principal Ricci curvatures is a Riemannian locally symmetric space.
