  We prove that the Hopf vector field is a unique one among geodesic
covariantly normal unit vector fields on spheres such that the submanifold
generated by the field is totally geodesic in the unit tangent bundle with
Sasaki metric. As application, we give a new proof of stability (instability)
of the Hopf vector field with respect to volume variation using standard
approach from the theory of submanifolds and find exact boundaries for the
sectional curvature of the Hopf vector field.
