Second Order Parallel Tensors on Almost Kenmotsu Manifolds Satisfying the Nullity Distributions

Abstract. In this paper, we prove that if there exists a second order symmetric parallel tensor on an almost Kenmotsu manifold (M2n+1, φ, ξ, η, 1) whose characteristic vector field ξ belongs to the (k, µ)′-nullity distribution, then either M2n+1 is locally isometric to the Riemannian product of an (n + 1)-dimensional manifold of constant sectional curvature −4 and a flat n-dimensional manifold, or the second order parallel tensor is a constant multiple of the associated metric tensor of M2n+1. Furthermore, some properties of an almost Kenmotsu manifold admitting a second order parallel tensor with ξ belonging to the (k, µ)-nullity distribution are also obtained. 1