xi(perpendicular to)-submanifolds of para-Sasakian manifolds

Almost semiinvariant xi(perpendicular to)-submanifolds of an almost paracontact metric manifold are defined and studied. Some characterizations of almost semiinvariant xi(perpendicular to)-submanifolds and semiinvariant xi(perpendicular to)-submanifolds are presented. A para-CR-structure is defined and it is proven that an almost semiinvariant xi(perpendicular to)-submanifold of a normal almost paracontact metric (and hence para-Sasakian) manifold with the proper invariant distribution always possesses a para-CR-structure. A counter example is also given. Integrability conditions for certain natural distributions arising on almost semiinvariant xi(perpendicular to)-submanifolds are obtained. Finally, certain parallel operators on submanifolds are investigated.