Complex conformal submersions with total space a locally conformal Kähler manifold

Abstract

In this paper we study almost complex conformal submersions with total space a locally conformal Kahler (l.c.K.) manifold, which we call l.c.K. tau-conformal submersions. We derive necessary and sufficient conditions for the horizontal distribution of a l.c.K. tau-conformal submersion to be completely integrable. We also obtain necessary and sufficient conditions for the base space to be a Kahler manifold and for the fibers to be minimal. Finally, we give some examples.