On the geometry of almost contact metric manifolds of Kenmotsu type

摘要

We analyze the Riemannian geometry of almost α-Kenmotsu manifolds, focusing on local symmetries and on some vanishing conditions for the Riemannian curvature. If the characteristic vector field of an almost α-Kenmotsu structure belongs to the so-called (Κ,μ)'-nullity distribution, Κ<-α2, then the Riemannian curvature is completely determined. These manifolds provide a special case of a wider class of almost α-Kenmotsu manifolds, for which an operator h' associated to the structure is η-parallel and has constant eigenvalues. All these manifolds are locally warped products. Finally, we give a local classification of almost α-Kenmotsu manifolds, up to D-homothetic deformations. Under suitable conditions, they are locally isomorphic to Lie groups.