Semi-slant and bi-slant submanifolds of almost contact metric 3-structure manifolds

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