On the geometry of almost contact metric manifolds of Kenmotsu type

Abstract

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 < − α 2 , 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.