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? -submanifolds of para-Sasakian manifolds
(Turkish Journal of Mathematics, 2014) Yuksel, Selcen Perktas; Trıpathı, Mukut Mani; Kılıç, Erol; Keleş, Sadık
Abstract: Almost semiinvariant ξ ⊥ -submanifolds of an almost paracontact metric manifold are defined and studied. Some characterizations of almost semiinvariant ξ ⊥ -submanifolds and semiinvariant ξ ⊥ -submanifolds are presented. A para-CR-structure is defined and it is proven that an almost semiinvariant ξ ⊥ -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 ξ ⊥ -submanifolds are obtained. Finally, certain parallel operators on submanifolds are investigated.