The structure of Einstein spaces admitting conformal motions

An Einstein manifold that admits non-homothetic conformal Killing vector fields and is not Ricci flat has locally the structure of a warped product, provided that the span of the set of closed conformal vector fields is non-degenerate and has constant dimension. The fibre of this warped product is Einstein, while the base has constant sectional curvature. At each point, the set of closed conformal vector fields spans the tangent space to the base.