  Sub-Riemannian structures on odd-dimensional spheres respecting the Hopf
fibration naturally appear in quantum mechanics. We study the curvature maps
for such a sub-Riemannian structure and express them using the Riemannian
curvature tensor of the Fubini-Study metric of the complex projective space and
the curvature form of the Hopf fibration. We also estimate the number of
conjugate points of a sub-Riemannian extremal in terms of the bounds of the
sectional curvature and the curvature form. It presents a typical example for
the study of curvature maps and comparison theorms for a general corank 1
sub-Riemannian structure with symmetries done by C.Li and I.Zelenko.
