Principal toroidal bundles over Cauchy-Riemann products

Abstract

The main result we obtain is that given π:N→M a Ts-subbundle of the generalized Hopf fibration π¯:H2n+s→ℂPn over a Cauchy-Riemann product i:M⊆ℂPn, i.e. j:N⊆H2n+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 H2n+s then N is a Cauchy-Riemann submanifold whose Chen class is non-vanishing.