Almost contact submersions with total space a locally conformal cosymplectic manifold

Abstract

In this paper we study almost contact metric submersions with total space a locally conformal cosymplectic manifold. We obtain some results on the minimality of the fibers, transference of the In this paper we study almost contact metric submersions with total space a locally conformal cosymplectic manifold. We obtain some results on the minimality of the fibers, transference of the almost contact metric structure to the base manifold, the induced structure on the fibers, and on the integrability of the horizontal distribution. We obtain the local model of locally conformal cosymplectic submersion with totally umbilical fibers and we show that the total space of a locally conformal cosymplectic submersion cannot be a PC-manifold (i.e. a particular class of locally conformal cosymplectic manifold which is foliated by generalized Hopf manifolds). Although, we obtain examples of almost contact submersions (which are not Riemannian submersions) with total space a PC-manifold. These examples suggest us to define the D(03C3)-conformal cosymplectic submersions. Necessary and sufficient conditions for the fibers of a such submersion to be minimal and for the horizontal distribution to be completely integrable are derived. A particular class of D(03C3)-conformal cosymplectic submersion which is in certain sense, analogous to a trivial cosymplectic submersion is studied and is obtained that this submersion is the model of D(03C3)-conformal cosymplectic submersion with totally umbilical fibers and horizontal Lee vector field. Finally, we study D(03C3)-conformal cosymplectic submersions with total space a PC-manifold. We obtain all the D(03C3)-conformal cosymplectic submersions with totally geodesic fibers and total space a particular class of PC-manifolds. of almost contact submersions (which are not Riemannian submersions) with total space a PC-manifold. These examples suggest us to define the D(03C3)-conformal cosymplectic submersions. Necessary and sufficient conditions for the fibers of a such submersion to be minimal and for the horizontal distribution to be completely integrable are derived. A particular class of D(03C3)-conformal cosymplectic submersion which is in certain sense, analogous to a trivial cosymplectic submersion is studied and is obtained that this submersion is the model of D(03C3)-conformal cosymplectic submersion with totally umbilical fibers and horizontal Lee vector field. Finally, we study D(03C3)-conformal cosymplectic submersions with total space a PC-manifold. We obtain all the D(03C3)-conformal cosymplectic submersions with totally geodesic fibers and total space a particular class of PC-manifolds.