On some moment maps and induced Hopf bundles in the quaternionic projective space

We describe a diagram containing the zero sets of the moment maps associate d to the diagonal U(1) and Sp(1) actions on the quaternionic projective spa ce HPn. These sets are related both to focal sets of submanifolds and to Sa sakian-Einstein structures on induced Hopf bundles. As an application, we c onstruct a complex structure on the Stiefel manifolds V-2(Cn+l) and (V) ove r tilde (4)(Rn+1), the one on the former manifold not being compatible with its known hypercomplex structure.