We study the holomorphic structure of certain complex manifolds associated with W algebras, namely, the flag manifolds W/T and W1+/T1+, and the spaces W/SL(),R) and W1+/GL(,R), where T and T1+ are the maximal tori in W and W1+. We compute their Ricci curvature and show how the results are related to the anomaly-freedom conditions for W and W1+. We discuss the relation of these manifolds with extensions of universal Teichmller space. 1991 Springer-Verlag.
