Lightlike hypersurfaces in indefinite S-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 f -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, we obtain an indefinite S-structure on the leaves of an integrable distribution. The existence of totally umbilical lightlike hypersurfaces of an indefinite S-space form is also discussed. Finally, we explicitely describe a lightlike hypersurface of an indefinite S-manifold. 2000 Mathematics Subject Classification 53C40, 53C50, 53D10