Principal toroidal bundles over Cauchy-Riemann products

Abstract

The main result we obtain is that givenπ:N→MaTs-subbundle of the generalized Hopf fibrationπ¯:H2n+s→ℂPnover a Cauchy-Riemann producti:M⊆ℂPn, i.e.j:N⊆H2n+sis a diffeomorphism on fibres andπ¯∘j=i∘π, ifsis even andNis a closed submanifold tangent to the structure vectors of the canonicalℊ-structure onH2n+sthenNis a Cauchy-Riemann submanifold whose Chen class is non-vanishing.