Locally conformal Kähler submersions (Q1337119)

Almost Hermitian submersions with total space a locally conformal Kähler manifold are called locally conformal Kähler submersions. The authors derive necessary and sufficient conditions for the fibers of such a submersion to be minimal and for the horizontal distribution to be completely integrable. As a consequence they point out that a result of \textit{E. Musso} [Boll. Unione Mat. Ital., VII. Ser., A 3, No. 2, 171-176 (1989; Zbl 0679.53055)] is not true in general. Moreover: (1) some relations between the Betti numbers of the total space and the base space are deduced, especially when the fibers are totally geodesic submanifolds; (2) the transfer of structures and some geometric properties on locally conformal Kähler submersions with total space a generalized Hopf manifold are studied; and (3) all the locally conformal Kähler submersions with totally geodesic fibers and total space a particular class of generalized Hopf manifolds are obtained.