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f -structures of Kenmotsu type. (English) Zbl 1167.53306

Summary: 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

𝒯 1 𝒯 2

of the classification stated by Tricerri and Vanhecke, provided that it is a locally symmetric space.

MSC:
53C15Differential geometric structures on manifolds
53D15Almost contact and almost symplectic manifolds
53C25Special Riemannian manifolds (Einstein, Sasakian, etc.)