Ricci Recurrent Almost Kenmotsu 3-Manifolds

Abstract

In this paper, we obtain that a Ricci recurrent 3-dimensional almost Kenmotsu manifold with constant scalar curvature satisfying $\nabla_\xi h=0$, $h\neq0$, is locally isometric to the Riemannian product $\mathbb{H}^2(-4)\times\mathbb{R}$.