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Turkish Journal of Mathematics

Abstract

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.

DOI

10.3906/mat-1307-13

Keywords

Almost paracontact metric manifold, para-Sasakian manifold, \xi^{\perp}-submanifold, almost semiinvariant \xi^{\perp}-submanifolds, para-CR-structure.

First Page

905

Last Page

919

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