Even-Dimensional Slant Submanifolds of a C 5 ⊕ C 12 -Manifold

We studied isometric immersions into an almost contact metric manifold which falls in the Chinea–Gonzalez class C5⊕C12, under the hypothesis that the Reeb vector field of the ambient space is normal to the considered submanifolds. Particular attention to the case of a slant immersion is paid. We relate immersions into a Kähler manifold to suitable submanifolds of a C5⊕C12-manifold. More generally, in the framework of Gray–Hervella, we specify the type of the almost Hermitian structure induced on a non anti-invariant slant submanifold. The cases of totally umbilical or austere submanifolds are discussed.