f-Structures of Kenmotsu Type

Abstract.

A class of manifolds which admit an f-structure with s-dimensional parallelizable kernel is introduced and studied. Such manifolds are Kenmotsu manifolds if s  =  1, and carry a locally conformal Kähler structure of Kashiwada type when s = 2. The existence of several foliations allows to state some local decomposition theorems. The Ricci tensor together with Einstein-type conditions and f-sectional curvatures are also considered. Furthermore, each manifold carries a homogeneous Riemannian structure belonging to the class $\mathcal{T}_{1} \oplus \mathcal{T}_{2}$ of the classification stated by Tricerri and Vanhecke, provided that it is a locally symmetric space.