Note about characteristic lightlike hypersurfaces of indefinite globally framed /-manifolds

In a metric g f f-manifold we study lightlike hypersurfaces M tangent to the characteristic vector fields, and owing to the presence of the /-structure, we determine some decompositions of TM and of a chosen screen distribution obtaining two distributions invariant with respect to the structure. We discuss the existence of a g f f-structure on a lightlike hypersurface and, under suitable hypotheses, the existence of totally umbilical lightlike hypersurfaces of an indefinite psi-space form.