Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 5
x\perp-submanifolds of para-Sasakian manifolds
- Pages
- 905–919
- DOI
- —
Abstract
Almost semiinvariant x\perp-submanifolds of an almost paracontact metric manifold are defined and studied. Some characterizations of almost semiinvariant x\perp-submanifolds and semiinvariant x\perp-submanifolds are presented. A para-CR-structure is defined and it is proven that an almost semiinvariant x\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 x\perp -submanifolds are obtained. Finally, certain parallel operators on submanifolds are investigated.
Özet
Almost semiinvariant x\perp-submanifolds of an almost paracontact metric manifold are defined and studied. Some characterizations of almost semiinvariant x\perp-submanifolds and semiinvariant x\perp-submanifolds are presented. A para-CR-structure is defined and it is proven that an almost semiinvariant x\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 x\perp -submanifolds are obtained. Finally, certain parallel operators on submanifolds are investigated.