Anna Maria Pastore

Maps Interchanging f-Structures and their Harmonicity

We study some remarkable classes of metric f-structures on differentiable manifolds (namely, almost Hermitian, almost contact, almost S-structures and K-structures). We state and prove the necessary condition(s) for the existence of maps commuting such structures. The paper contains several new results, of geometric significance, on CR-integrable manifolds and the harmonicity of such maps.

Note about characteristic lightlike hypersurfaces of indefinite globally framed f‐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, the existence of totally umbilical lightlike hypersurfaces of an indefinite I‐space form.