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‎In this paper‎, ‎invariant and‎ ‎anti-invariant submanifolds of Sasakian statistical manifolds are studied‎. ‎Necessary and sufficient conditions are given for vanishing the dual connection in the normal bundle‎. ‎Moreover‎, ‎existence of a Kaehlerian structure on invariant hypersurfaces of Sasakian statistical manifolds are proved‎.

In this paper, we introduce point-wise slant submanifolds of almost contact and almost contact 3-structure manifolds. We characterize them, give some examples, and obtain necessary and sufficient conditions for a point-wise slant submanifold of a 3-Sasakian manifold to be a slant submanifold. Moreover, we show that there exist no proper Sasakian point-wise 3-slant submanifolds.

In this paper we introduce the notion of slant submanifold of an almost contact metric 3-structure manifold. We give some examples and characterize these submanifolds. Moreover, Sasakian slant submanifolds of an almost contact 3-structure manifold are defined and studied. We also establish a sharp inequality including the squared mean curvature and Ricci curvature of a Sasakian slant submanifold.

In this paper we introduce the notions of semi-slant and bi-slant submanifolds of an almost contact 3-structure manifold. We give some examples and characterization theorems about these submanifolds. Moreover, the distributions of semi-slant submanifolds of 3-cosymplectic and 3-Sasakian manifolds are studied. ϕi)i=1;2;3 and the vector elds should be slant or invariant with respect to all of the ϕi's. Therefore, it is a generalization of invariant, anti-invariant, slant, semi-slant, and bi-slant submanifolds in almost contact metric 3-structures and we denote them by 3- semi-slant and 3-bi-slant submanifolds. Following the approaches of (3, 13), we characterized 3-bi-slant and 3-semi-slant submanifolds and studied geometric properties of distributions of these submanifolds where the ambient manifolds are 3-Sasakian or 3-cosymplectic. It should be noted that, in the denition of semi-slant