Homogeneous Conformal String Backgrounds

We present exact solutions characterised by Bianchi-type I, II, III, V, VI 0 , VI h four-dimensional metric, space-independent dilaton, and vanishing torsion background, for the low energy string eeective action with zero central charge deecit. We show that, in such a context, curvature singularities cannot be avoided, except for the trivial case of at spacetime and constant dilaton. We also provide a further example of the failure of the standard prescription for connecting conformal string backgrounds through duality transformations associated to non-semisimple, non-Abelian isometry groups.