On a higher dimensional generalization of Seifert fibrations

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