  For any natural $k \leq n$, the rational cohomology ring of the space of
continuous maps $S^{2k-1} \to S^{2n-1}$ (respectively, $S^{4k-1} \to S^{4n-1}$)
equivariant under the Hopf action of the circle (respectively, of the group
$S^3$ of unit quaternions) is naturally isomorphic to that of the Stiefel
manifold $V_k({\mathbb C}^n)$ (respectively, $V_k({\mathbb H}^n)$).
