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Full-Text Articles in Physical Sciences and Mathematics
\Xi^{\Perp}-Submanifolds Of Para-Sasakian Manifolds, Selcen Yüksel Perktaş, Mukut Mani Tripathi, Erol Kiliç, Sadik Keleş
\Xi^{\Perp}-Submanifolds Of Para-Sasakian Manifolds, Selcen Yüksel Perktaş, Mukut Mani Tripathi, Erol Kiliç, Sadik Keleş
Turkish Journal of Mathematics
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.
Paracontact Semi-Riemannian Submersions, Yilmaz Gündüzalp, Bayram Şahi̇n
Paracontact Semi-Riemannian Submersions, Yilmaz Gündüzalp, Bayram Şahi̇n
Turkish Journal of Mathematics
In this paper, we first define the concept of paracontact semi-Riemannian submersions between almost paracontact metric manifolds, then we provide an example and show that the vertical and horizontal distributions of such submersions are invariant with respect to the almost paracontact structure of the total manifold. The study is focused on fundamental properties and the transference of structures defined on the total manifold. Moreover, we obtain various properties of the O'Neill's tensors for such submersions and find the integrability of the horizontal distribution. We also find necessary and sufficient conditions for a paracontact semi-Riemannian submersion to be totally geodesic. Finally, …