The main result we obtain is that given π : N → M a T s -subbundle of the generalized Hopf fibration π ¯ : H 2 n + s → ℂ P n over a Cauchy-Riemann product i : M ⊆ ℂ P n , i.e. j : N ⊆ H 2 n + s is a diffeomorphism on fibres and π ¯ ∘ j = i ∘ π , if s is even and N is a closed submanifold tangent to the structure vectors of the canonical ℊ -structure on H 2 n + s then N is a Cauchy-Riemann submanifold whose Chen class is non-vanishing.