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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 \[ \mathcal{T}_{1} \oplus \mathcal{T}_{2} \] of the classification stated by Tricerri and Vanhecke, provided that it is a locally symmetric space.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53D15 Almost contact and almost symplectic manifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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