On 4-Dimensional Submanifolds of f-Manifolds

The present paper is devoted to a class of manifolds which admit an f-structure with 2-dimensional parallelizable kernel. Such manifolds are called 4-dimensional almost bi-contact metric manifolds; they carry a locally conformal almost Kähler structure. We give some classifications and prove their fundamental properties, then we deduce some properties about the complex manifolds associated with them. We show the existence of such manifolds by giving some non-trivial examples. Finally, we establish an interesting class and construct a concrete example.