ξ^⊥-submanifolds of para-Sasakian manifolds

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