Falcitelli, Maria; Pastore, Anna Maria \(f\) -structures of Kenmotsu type. (English) Zbl 1167.53306 Mediterr. J. Math. 3, No. 3-4, 549-564 (2006). 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. Cited in 4 Documents 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.) Keywords:\(f\)-structure; Kenmotsu manifold; \(\eta \)-Einstein manifold; curvature; homogeneous structure PDFBibTeX XMLCite \textit{M. Falcitelli} and \textit{A. M. Pastore}, Mediterr. J. Math. 3, No. 3--4, 549--564 (2006; Zbl 1167.53306) Full Text: DOI