Slant immersions in $C_5$-manifolds

Odd-dimensional non anti-invariant slant submanifolds of an α- Kenmotsu manifold are studied. We relate slant immersions into a Kähler manifold with suitable slant submanifolds of an α-Kenmotsu manifold. More generally, in the framework of Chinea-Gonzalez, we specify the type of the almost contact metric structure induced on a slant submanifold, then stating a local classification theorem. The case of austere immersions is discussed. This helps in proving a reduction theorem of the codimension. Finally, slant submanifolds which are generalized Sasakian space-forms are described