Even-Dimensional Slant Submanifolds of a $$\varvec{C_5\oplus C_{12}}$$ C 5 ⊕ C 12 -Manifold

Abstract

We studied isometric immersions into an almost contact metric manifold which falls in the Chinea–Gonzalez class $$C_5\oplus C_{12}$$ , 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 Kahler manifold to suitable submanifolds of a $$C_5\oplus C_{12}$$ -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.