On a high-dimensional generalization of Seifert fibrations

The notion of generalized Seifert fibration is introduced, it is shown that the projections of certain Eschenburg $7$-manifolds onto $\mathbb{C}{P}^2$ define such fibrations, and for them the characteristic classes corresponding to the generators of $H^2(B(U(2)\mathrm{/}{\mathbb{Z}}_{2n});\mathbb{Z})$ are defined.