On the geometry of almost contact metric manifolds of Kenmotsu type

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)′(κ,μ)′-nullity distribution, κ<−α2κ<−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′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 DD-homothetic deformations. Under suitable conditions, they are locally isomorphic to Lie groups.