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We describe a diagram containing the zero sets of the moment maps associated to the diagonal U(1) and Sp(1) actions on the quaternionic projective space ℍPn. These sets are related both to focal sets of submanifolds and to Sasakian–Einstein structures on induced Hopf bundles. As an application, we construct a complex structure on the Stiefel manifolds $V_2(\mathbb{C}^{n+1})$ and $\tilde V_4({\mathbb R}^{n+1})$, the one on the former manifold not being compatible with its known hypercomplex structure.

ON SOME MOMENT MAPS AND INDUCED HOPF BUNDLES IN THE QUATERNIONIC PROJECTIVE SPACE