EXAMPLES OF CURVATURE HOMOGENEOUS LORENTZ METRICS

Examples of a three- and a four-dimensional Lorentz manifold are prese nted which are curvature homogeneous up to order one, without being lo cally homogeneous, in contrast to the situation in the Riemannian case , where a curvature homogeneity up to order one implies local homogene ity in the three- and four-dimensional cases. it is further shown that these manifolds satisfy the property that all scalar curvature invari ants vanish identically, i.e. are those of a flat Lorentz manifold. As an immediate consequence, we also obtain examples of Lorentz manifold s whose curvature invariants are all constant, but which are not local ly homogeneous, again in contrast to the Riemannian case where such ma nifolds are always locally homogeneous.